If the sum of n terms of an A. | Class 11 Mathematics Chapter Sequence and Series, Sequence and Series NCERT Solutions

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.

Answer:

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, $S subscript n space space end subscript equals space n over 2 open square brackets 2 a plus left parenthesis n minus 1 right parenthesis d close square brackets$

Here,

$n over 2 open square brackets 2 a plus n d minus d close square brackets equals 3 n squared plus 5 n rightwards double arrow n a space plus space n squared. d over 2 equals 3 n squared plus 5 n$

Comparing the coefficient of n2 on both sides, we obtain

$d over 2 equals 3 rightwards double arrow d equals 6$

Comparing the coefficient of n on both sides, we obtain

$a minus d over 2 equals 5 rightwards double arrow a minus 3 equals 5 rightwards double arrow a equals 8$

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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Comments

Shivdas
2019-01-24 21:52:34

Fabulous effort

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Welcome to the NCERT Solutions for Class 11 Mathematics - Chapter . This page offers a step-by-step solution to the specific question from Excercise 2 , Question 13: If the sum of n terms of an A.P. is 3n2 + 5n and its mth term is 164, find ....

If the sum of n terms of an A. | Class 11 Mathematics Chapter Sequence and Series, Sequence and Series NCERT Solutions

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