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If the sum of n terms of an ap is 3n^2+5n and it's mth term is 164 find the value of m

Posted by Aditya Mukesh B. K. 2 years, 10 months ago

CBSE > Class 10 > Mathematics

1 answers

Preeti Dabral 2 years, 10 months ago

S_n = 3n² + 5n
Put n = 1, 2, 3,....
S₁ = 8
{tex}{S_2} = 3 \times 4 + 10 = 22{/tex}
a₁ = S₁ = 8
a₂ = S₂ - S₁
= 22 - 8 = 14
d = a₂ - a₁ = 14 - 8 = 6
a_m = 164
{tex} \Rightarrow {/tex} a + (m - 1)d = 164
{tex} \Rightarrow {/tex} 8 (m - 1) (6) = 164
{tex} \Rightarrow {/tex} 8 + 6m - 6 = 164
{tex} \Rightarrow {/tex} 6m = 164 - 2
{tex} \Rightarrow {/tex} 6m = 162
{tex} \Rightarrow m = \frac{{162}}{6} = 27{/tex}

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