First slide

Arithmetic progression

Question

If the sum to n terms of an A.P. is $3 n^{2} + 5 n$ ,while
$T_{m} = 164$ then value of m is

Moderate

A

25
B

26
C

27
D

28

Solution

$\begin{array}{l} T_{m} = S_{m} - S_{m - 1} \\ \begin{aligned} \Rightarrow & 164 = 3 m^{2} + 5 m - [3 (m - 1)^{2} + 5 (m - 1) \\ = 6 m + 2 \end{aligned} \\ \Rightarrow m = 27 \end{array}$

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