NCERT Solutions for Class 10 Maths Chapter 5 – Arithmetic Progressions Exercise 5.2

NCERT Solutions for Class 10 Maths Chapter 5 – Arithmetic Progressions Exercise 5.2 are provided to help students with their Class 10 exam preparations. These solutions are carefully designed by subject experts to explain the application of arithmetic progressions in more complex scenarios. The exercise helps students practice the formulae and apply them to solve problems related to the sum of terms in an arithmetic progression.

Exercise 5.2 focuses on problems that require students to calculate the sum of n terms in an arithmetic progression given specific conditions. This includes using the formula for the sum of the first n terms and applying it to different contexts.

NCERT Solutions for Class 10 Maths Chapter 5 – Arithmetic Progressions Exercise 5.2

Arithmetic Progression
Medium
Q.
Fill in the blanks in the following table, given that a is the first term, d the common difference and an the nth term of the AP:
Arithmetic Progression
Medium
Q.
Two APs have the same common difference. The difference between their 100th terms is 100, what is the difference between their 1000th terms?
Arithmetic Progression
Easy
Q.
Show that (a−b)2,(a2+b2) and (a+b)2(a-b)^2,\left(a^2+b^2\right)\ \rm { and \ }(a+b)^2​ are in AP.
[CBSE - 2020]
Arithmetic Progression
Medium
Q.
How many terms of the AP : 9, 17, 25, . . . must be taken to give a sum of 636?
Arithmetic Progression
Medium
Q.
Find the 20th term from the last term of the AP: 3, 8, 13, . . ., 253.
Arithmetic Progression
Medium
Q.
Determine the AP whose third term is 16 and the 7th term exceeds the 5th term by 12.
Arithmetic Progression
Medium
Q.
For what value of n, are the nth terms of two APs: 63, 65, 67, . . . and 3, 10, 17, . . . equal?
Arithmetic Progression
Medium
Q.
How many multiples of 4 lie between 10 and 250?
Arithmetic Progression
Medium
Q.
How many three-digit numbers are divisible by 7?
Arithmetic Progression
Medium
Q.
Which term of the AP: 3, 15, 27, 39, . . . will be 132 more than its 54th term?
Arithmetic Progression
Medium
Q.
Choose the correct choice in the following and justify:(i) 30th term of the AP: 10, 7, 4, . . . , is     (A) 97     (B) 77      (C) −77      (D) −87(ii) 11th term of the AP: −3, −12, 2, . . ., is      (A) 28     (B) 22     (C) −38      (D) −4812 \begin{array}{l}{Choose the correct choice in the following and justify:}\\ {(i) 30th term of the AP: 10, 7, 4, . . . , is}\\ {     (A) 97     (B) 77      (C) }-{77      (D) }-{87}\\ {(ii) 11th term of the AP: }-{3, }\frac{-{1}}{2}{, 2, . . ., is}\\ {      (A) 28     (B) 22     (C) }-{38      (D) }-{48}\frac{1}{2}\end{array}
Arithmetic Progression
Medium
Q.
The 17th term of an AP exceeds its 10th term by 7. Find the common difference.
Arithmetic Progression
Medium
Q.
If the 3rd and the 9th terms of an AP are 4 and –8 respectively, which term of this AP is zero?
Arithmetic Progression
Medium
Q.
An AP consists of 50 terms of which 3rd term is 12 and the last term is 106. Find the 29th term.
Arithmetic Progression
Medium
Q.
Find the 31st term of an AP whose 11th term is 38 and the 16th term is 73.
Arithmetic Progression
Medium
Q.
Check whether –150 is a term of the AP: 11, 8, 5, 2, . . .
Arithmetic Progression
Medium
Q.
Which term of the AP: 3, 8, 13, 18, . . . , is 78?
Arithmetic Progression
Medium
Q.
InthefollowingAPs,findthemissingtermsintheboxes:(i)2,)‾,26(ii))‾,13,)‾,3(iii)5,)‾,)‾,912(iv)−4,)‾,)‾,)‾,)‾,6(v))‾,38,)‾,)‾,)‾,−22 \begin{array}{l}\mathrm{In}{\hspace{0.17em}}\mathrm{the}{\hspace{0.17em}}\mathrm{following}{\hspace{0.17em}}\mathrm{APs},{\hspace{0.33em}}\mathrm{find}{\hspace{0.17em}}\mathrm{the}{\hspace{0.17em}}\mathrm{missing}{\hspace{0.17em}}\mathrm{terms}{\hspace{0.17em}}\mathrm{in}{\hspace{0.17em}}\mathrm{the}{\hspace{0.17em}}\mathrm{boxes}:\\ \left(\mathrm{i}\right)\quad 2,{\hspace{0.17em}}\overline{)},{\hspace{0.17em}}26\\ \left(\mathrm{ii}\right)\quad \overline{)},{\hspace{0.17em}}13,{\hspace{0.17em}}\overline{)},{\hspace{0.17em}}3\\ \left(\mathrm{iii}\right)\quad 5,\quad \overline{)}{\hspace{0.17em}},\quad \overline{)}{\hspace{0.17em}},{\hspace{0.17em}}9\frac{1}{2}\\ \left(\mathrm{iv}\right)-4,{\hspace{0.17em}}\overline{)},\quad \overline{)}{\hspace{0.17em}},{\hspace{0.17em}}\overline{)},\quad \overline{)},{\hspace{0.17em}}6\\ \left(\mathrm{v}\right)\quad \overline{)},{\hspace{0.17em}}38,\quad \overline{)},\quad \overline{)}{\hspace{0.17em}},\quad \overline{)}{\hspace{0.17em}},{\hspace{0.17em}}-22\end{array}
Arithmetic Progression
Medium
Q.
Which term of the AP 3, 15, 27, 39, … will be 120 more than its 21st term?
[CBSE - 2019]

NCERT Solutions for Class 10 Maths Chapter 5 – Arithmetic Progressions Exercise 5.2

The solutions are aligned with the latest CBSE syllabus, providing step-by-step explanations and clear guidance to help students understand how to solve problems and build confidence in Arithmetic Progressions.

FAQs: Class 10 Maths Chapter 5 – Arithmetic Progressions Exercise 5.2

Q1. What is the focus of Exercise 5.2?
Answer:
Exercise 5.2 focuses on solving problems related to the sum of the first n terms of an arithmetic progression. It helps students apply the sum formula and solve problems in various contexts.

Q2. What is the formula for the sum of the first n terms of an AP?
Answer:
The sum of the first n terms of an arithmetic progression is given by the formula:

Sn=n2×[2a1+(n−1)×d]S_n = \frac{n}{2} \times \left[ 2a_1 + (n - 1) \times d \right]


or

Sn=n2×[a1+an]S_n = \frac{n}{2} \times \left[ a_1 + a_n \right]


where:

  • SnS_n is the sum of the first n terms,

  • a1a_1 is the first term,

  • ana_n is the nth term,

  • dd is the common difference,

  • nn is the number of terms.

Q3. How do I find the sum of n terms if the last term is given?
Answer:
If the last term

ana_n

is given, you can use the second formula for the sum of n terms:

Sn=n2×(a1+an)S_n = \frac{n}{2} \times (a_1 + a_n)


This is useful when you know the first term and the nth term but not the common difference.

Q4. How do NCERT Solutions help with exam preparation?
Answer:
These solutions provide step-by-step solutions and detailed explanations for solving problems related to sum of n terms in an arithmetic progression. By practicing these problems, students can gain confidence in using the formula and solving various types of AP problems, which is crucial for Class 10 exams.

Q5. How do I calculate the sum of the first n terms using the formula?
Answer:
To calculate the sum:

  1. Identify the first term

    a1a_1, the common difference

    dd, and the number of terms

    nn.

  2. Use the formula for the sum of the first n terms and substitute the values of

    a1a_1,

    dd, and

    nn into it.

  3. Simplify to find

    SnS_n, the sum of the first n terms.