NCERT Solutions for Class 10 Maths Exercise 5.4 Chapter 5 Arithmetic Progression - Future Study Point

NCERT Solutions for Class 10 Maths Exercise 5.4 Chapter 5 Arithmetic Progression

class 10 maths ex.5.4

NCERT Solutions for Class 10 Maths Exercise 5.4 Chapter 5 Arithmetic Progression

ex.5.4 class 10 maths

 

NCERT Solutions for Class 10 Maths Exercise 5.4 Chapter 5 Arithmetic Progression are presented here to boost preparation for the CBSE exam. NCERT Solutions for Class 10 Maths Exercise 5.4 Chapter 5 Arithmetic Progression are created here to boost preparation for the CBSE exam.NCERT Solutions for Class 10 Maths Exercise 5.4 Chapter 5 Arithmetic Progression is the best study material for the doubt clearance on chapter  5 – Arithmetic Progression. NCERT Solutions for Class 10 Maths Exercise 5.4 Chapter 5 Arithmetic Progression are valuable in anticipating the actual quantity in the field of financial matters, trade, science, and other problems when quantities are in a sequence.NCERT Solutions for Class 10 Maths Exercise 5.4 of Chapter 5 Arithmetic Progression are solved by an experienced CBSE maths teacher according to the standards of CBSE. All questions of exercise 5.4 are solved here by a step-by-step technique so every class 10 maths student can comprehend the solutions without any problem.

Class 10 Maths  Chapter 5 Arithmetic Progression contains four exercises, exercise 5.1, exercise 5.2, exercise 5.3, and exercise 5.4, here links of each exercise are given, so you can study NCERT solutions of whole Chapter 5 Arithmetic Progression.

Why are NCERT Solutions for Class 10 Maths Exercise 5.4 Chapter 5 Arithmetic Progression important for you?

  • All unsolved Questions of the exercise Exercise 5.4 are covered.
  • All questions are solved in detail by a step by step way.
  • These NCERT Solutions gives an idea about the way of solving the similar questions.
  • Exercise 5.4 covers the questions of 3-4 marks in class 10 maths board exam.

See the Video and subscribe,like and share –  NCERT Solutions for Class 10 Maths Exercise 5.4 Chapter 5 Arithmetic Progression

NCERT Solutions for Class 10 Maths Exercise 5.4 Chapter 5 Arithmetic Progression

Q1.Which term of the AP: 121, 117, 113, . . ., is its first negative term? [Hint: Find n for an < 0]

Ans. Let the first negative term of the given AP 121, 117, 113, . . ., is an

nth term of a AP is given by

an= a + (n -1)d

Where a = 121, d = 117 -121 =-4

For the first number to be negative

an< 0

a + (n -1)d < 0

121 + (n -1)×-4 <0

(n -1)×-4 < -121

-4n +4 < -121

4n -4 > 121

4n > 121 +4

4n > 125

n > 125/4

n > 31.25

Since n is a natural number therefore first negative term is 32 nd 

Q2.The sum of the third and the seventh terms of an AP is 6 and their product is 8. Find the sum of the first sixteen terms of the AP.

Ans.The sum of third and seventh terms of an AP is 6

a3+ a7=6

a +2d +a +6d =6

2a +8d =6

a + 4d = 3……(i)

a3× a7=8

(a +2d )(a +6d) = 8

Putting the value of a from the equation (i) a =3 -4d

(3-4d +2d )(3-4d +6d) = 8

(3 -2d )(3 +2d) = 8

9 – 4d² = 8

4d² = 9-8 =1

d² = 1/4

d =±(1/2)

Putting d =1/2 in equation (i)

a + 4×1/2 = 3

a +2 =3

a = 1

Putting d =-1/2 in equation (i)

a + 4×-1/2 = 3

a -2 =3

a = 5

If d=1/2,a=1 then the sum of n terms of the AP is given by

Sn= n/2[2a + (n – 1)d]

=16/2[2×1 + (16 – 1)×1/2]

=8[2 +15/2]

=8×(4+15)/2=4×19 =76

If d=-1/2,a=5 then the sum of n terms of the AP is given by

Sn= n/2[2a + (n – 1)d]

=16/2[2×5 + (16 – 1)×-1/2]

=8[10 -15/2]

=8×(20-15)/2=4×5=20

Q3.A ladder has rungs 25 cm apart. (see Fig. 5.7). The rungs decrease uniformly in length from 45 cm at the bottom to 25 cm at the top. If the top and the bottom rungs are     
 apart, what is the length of the wood required for the rungs? [Hint: Number of rungs = 250/25 +1].

Q3 Class 10 maths AP exercise 5.4

Ans.The distance the top and the bottom rungs is

The rungs are 25 cm distance apart

The number of rungs in the ladder

250/25 +1  =10 + 1 =11

Since the rungs decrease uniformly in length from 45 cm at the bottom to 25 cm at the top,the length between the successive rungs has a common difference therefore the lengths of rungs make an AP.

45,45 +d, 45 +2d+……..25

First term,a =45 and last term,l =25

The sum of the AP shows  the length of the wood required for the rungs

Sn=n/2[a +l]

= 11/2[45 +25]

=11/2[70] =11×35 =385

Hence the length of the wood required for the rungs is 385 cm

NCERT Solutions for Class 10 Maths Exercise 5.4 Chapter 5 Arithmetic Progression

Q4.The houses of a row are numbered consecutively from 1 to 49. Show that there is a value of x such that the sum of the numbers of the houses preceding the house numbered x is equal to the sum of the numbers of the houses following it. Find this value of x. [Hint :Sx – 1 = S49 – Sx ]

Ans.It is given that houses are numbered from 1 to 49 and house no. x is such that the sum of the numbers of the houses preceding the house numbered x is equal to the sum of the numbers of the houses following it.

1,2,3……….x-1,x,x+1…………49

Since the sum of the numbers of the houses preceding the house numbered x is equal to the sum of the numbers of the houses following it.

Number of the houses preceding the number x are (x -1) and the number of houses following the number x are 49 -x

Given to us

Sx-1=S49-x

The sum of n terms of the AP is given by

Sn=n/2[a +l]

=(x-1)/2[1 +x-1]=x(x -1)/2

S49-x=(49-x)/2 [x+1 +49]=(49-x)/2[x+50]

x(x -1)/2 = (49-x)/2[x+50] =(49x +2450 -x²-50x)/2

x² -x = 49x +2450 -x²-50x

2x² -x +50x -49x – 2450 =0

2x² -2450

2x² = 2450

x² = 2450/2 =1225

x = ±35

Neglecting the negative term because the number of houses can’t be negative,therefore x =35

Q5.A small terrace at a football ground comprises of 15 steps each of which is 50 m long and built of solid concrete. Each step has a rise of 1 /4 m and a tread of 1 /2 m. (see Fig. 5.8). Calculate the total volume of concrete required to build the terrace. [Hint : Volume of concrete required to build the first step = 1/4 ×1/2 ×50 m3.]

Q5,exercise 5.4 class 10

Ans. The terrace has 15 steps, each step has a rise of 1 /4 m and a tread of 1 /2 m

The height of the first step, second step, third step up to 15 th step  from the ground  is

1/4 m, (1/4 m +1/4 m),…………,[1/4+(15-1)1/4]m=1/4 +7/2

⇒1/4 m,1/2 m,3/4 m……,15/4 m

Length × breadth of each step are 50 m ×1/2 m

The volumes of the concrete required for first, second, third up to 15 th step are

(1/4×50  ×1/2 )m³,(1/2×50  ×1/2 )m³,(3/4×50  ×1/2 )m³,…….(15/4×50  ×1/2 )m³

(50/8)m³,(50/4)m³,(150/8)m³……..,(750/8)m³

6.25 m³, 12.5 m³,18.75m³……..,93.75 m³

Since the terms show that it is an AP, therefore total volume of the terrace will be the sum of the AP

The sum of n terms of the AP is given by

Sn=n/2[a +l]

Putting the value n =15,a =6.25, l =93.75

S15=15/2[6.25 +93.75] =15/2[100] =15×50 =750

Hence the total volume of concrete required to build the terrace is 750 m³

The formulas used in this exercise 5.4 are following

nth term of an AP is given by

an is nth term of the AP, d is common difference of the AP, n is total number of terms

Sum of the n terms is given by

Sn is the n terms of the AP

We hope you would have liked the solutions of the class 10 maths exercise 5.4 Arithmetic Progression,the questions of exercise 5.4 are very important not only for the preparation of class 10 maths paper in term 2 CBSE Board exam but also useful in the preparation of competitive entrance exams. If you liked the solutions then please don’t forget to subscribe share our website for updated information because without your support we can’t survive on the web.

You can compensate us by donating any amount of money for our survival

Our Paytm NO 9891436286

NCERT Solutions for Class 10 Maths  Chapter 5 Arithmetic Progression

Class 10 Maths Exercise 5.1 Arithmetic Progression

Class 10 Maths Exercise 5.2 Arithmetic Progression

Class 10 Maths Exercise 5.3 Chapter 5 Arithmetic Progression

Important Questions of Class 10 Maths Chapter 5-Arithmetic Progression

NCERT Solutions for Class 10 Maths  Chapter 13 -Surface areas and Volumes(Term 2)

NCERT Solutions of  Science and Maths for Class 9,10,11 and 12

NCERT Solutions of class 9 science 

Chapter 1-Matter in our surroundingsChapter 9- Force and laws of motion
Chapter 2-Is matter around us pure?Chapter 10- Gravitation
Chapter3- Atoms and MoleculesChapter 11- Work and Energy
Chapter 4-Structure of the AtomChapter 12- Sound
Chapter 5-Fundamental unit of lifeChapter 13-Why do we fall ill ?
Chapter 6- TissuesChapter 14- Natural Resources
Chapter 7- Diversity in living organismChapter 15-Improvement in food resources
Chapter 8- MotionLast years question papers & sample papers

CBSE Class 9-Question paper of science 2020 with solutions

CBSE Class 9-Sample paper of science

CBSE Class 9-Unsolved question paper of science 2019

NCERT Solutions of class 10 maths

Chapter 1-Real numberChapter 9-Some application of Trigonometry
Chapter 2-PolynomialChapter 10-Circles
Chapter 3-Linear equationsChapter 11- Construction
Chapter 4- Quadratic equationsChapter 12-Area related to circle
Chapter 5-Arithmetic ProgressionChapter 13-Surface areas and Volume
Chapter 6-TriangleChapter 14-Statistics
Chapter 7- Co-ordinate geometryChapter 15-Probability
Chapter 8-Trigonometry

CBSE Class 10-Question paper of maths 2021 with solutions

CBSE Class 10-Half yearly question paper of maths 2020 with solutions

CBSE Class 10 -Question paper of maths 2020 with solutions

CBSE Class 10-Question paper of maths 2019 with solutions

NCERT solutions of class 10 science

Chapter 1- Chemical reactions and equationsChapter 9- Heredity and Evolution
Chapter 2- Acid, Base and SaltChapter 10- Light reflection and refraction
Chapter 3- Metals and Non-MetalsChapter 11- Human eye and colorful world
Chapter 4- Carbon and its CompoundsChapter 12- Electricity
Chapter 5-Periodic classification of elementsChapter 13-Magnetic effect of electric current
Chapter 6- Life ProcessChapter 14-Sources of Energy
Chapter 7-Control and CoordinationChapter 15-Environment
Chapter 8- How do organisms reproduce?Chapter 16-Management of Natural Resources

Solutions of class 10 last years Science question papers

CBSE Class 10 – Question paper of science 2020 with solutions

CBSE class 10 -Latest sample paper of science

NCERT solutions of class 11 maths

Chapter 1-SetsChapter 9-Sequences and Series
Chapter 2- Relations and functionsChapter 10- Straight Lines
Chapter 3- TrigonometryChapter 11-Conic Sections
Chapter 4-Principle of mathematical inductionChapter 12-Introduction to three Dimensional Geometry
Chapter 5-Complex numbersChapter 13- Limits and Derivatives
Chapter 6- Linear InequalitiesChapter 14-Mathematical Reasoning
Chapter 7- Permutations and CombinationsChapter 15- Statistics
Chapter 8- Binomial Theorem Chapter 16- Probability

CBSE Class 11-Question paper of maths 2015

CBSE Class 11 – Second unit test of maths 2021 with solutions

NCERT solutions of class 12 maths

Chapter 1-Relations and FunctionsChapter 9-Differential Equations
Chapter 2-Inverse Trigonometric FunctionsChapter 10-Vector Algebra
Chapter 3-MatricesChapter 11 – Three Dimensional Geometry
Chapter 4-DeterminantsChapter 12-Linear Programming
Chapter 5- Continuity and DifferentiabilityChapter 13-Probability
Chapter 6- Application of DerivationCBSE Class 12- Question paper of maths 2021 with solutions
Chapter 7- Integrals
Chapter 8-Application of Integrals

We hope you will like NCERT Solutions for Class 10 Maths Exercise 5.4 Chapter 5 Arithmetic Progression therefore please don’t forget to write your feedback, your feedback is necessary for us to improve, and you can suggest us recommendations for any kind of maths and science content.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Scroll to Top