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Question
If the sum of n terms of an A.P., is 3 n2 + 5 n then which of its terms is 164?
Options
26th
27th
28th
none of these.
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Solution
27th
\[S_n = 3 n^2 + 5n\]
\[ S_1 = 3 \left( 1 \right)^2 + 5\left( 1 \right) = 8\]
\[ \therefore a_1 = 8\]
\[ S_2 = 3 \left( 2 \right)^2 + 5\left( 2 \right) = 22\]
\[ \therefore a_1 + a_2 = 22\]
\[ \Rightarrow a_2 = 14\]
\[\text { Common difference, } d = 14 - 8 = 6\]
\[\text { Also, } a_n = 164\]
\[ \Rightarrow a + \left( n - 1 \right)d = 164\]
\[ \Rightarrow 8 + \left( n - 1 \right)6 = 164\]
\[ \Rightarrow n = 27\]
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