# Class 11 Mathematics Sequence and Series: NCERT Solutions for Question 13

This page focuses on the detailed Sequence and Series question answers for Class 11 Mathematics Sequence and Series, addressing the question: 'If the sum of n terms of an A.P. is 3n2 + 5n and its mth term is 164, find the value of m.'. The solution provides a thorough breakdown of the question, highlighting key concepts and approaches to arrive at the correct answer. This easy-to-understand explanation will help students develop better problem-solving skills, reinforcing their understanding of the chapter and aiding in exam preparation.
Question 13

## If the sum of n terms of an A.P. is 3n2 + 5n and its mth term is 164, find the value of m.

Let a and b be the first term and the common difference of the A.P. respectively.

am = a + (m – 1)d = 164 … (1)

Sum of n terms,

Here,

Comparing the coefficient of n2 on both sides, we obtain

Comparing the coefficient of n on both sides, we obtain

Therefore, from (1), we obtain

8 + (m – 1) 6 = 164

⇒ (m – 1) 6 = 164 – 8 = 156

⇒ – 1 = 26

⇒ m = 27

Thus, the value of m is 27.