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 3n^{2} + 5n and its *m*th term is 164, find the value of *m*.

Answer

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

*a**m* = *a* + (*m* – 1)*d* = 164 … (1)

Sum of *n* terms,

Here,

Comparing the coefficient of *n*2 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

⇒ *m *– 1 = 26

⇒ *m* = 27

Thus, the value of *m* is 27.

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Shivdas
2019-01-24 21:52:34

Fabulous effort

- NCERT Chapter