Question

If the sum of nth term of ap is 3n²+5n then which term of ap will be 164

Answer 1

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$in \: an \: ap \: given \: s _{n} = 3n {}^{2} + 5n \: \\ and \: a _{k} = s _{k} - s _{k - 1} \\ \implies \:a _{k } = (3k {}^{2} + 5k) - (3(k - 1) ^{2} + 5(k - 1)) \\ \implies a_{k} = (3k {}^{2} + 5k) - (3k {}^{2} - 6k + 3 + 5k - 5) \\ \implies \: a _{k} = 6k + 2 \\ according \: to \: given \: \: a _{k} = 164 \: \\ \implies6k + 2 = 164 \implies6k = 162 \implies \: k \: = 27$