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If the sum of n terms …

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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
  • 1 answers

Preeti Dabral 1 year, 11 months ago

Sn = 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
am = 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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