Question

In an AP if Sn = 3n^2 +5n and ak=164 find value of k.​

Answer 1

Answer: 27

Step-by-step explanation:given Sn=3n^2 + 5n

S1 = 3(1)^2 + 5(1)

= 3+5 =8

S2 = 3(2)^2 + 5(2)

= 12 + 8

= 22

a1 = 8

a2 = 22-8

= 14

a = 8

d = 6

ak = 164

ak = a + (k-1)d

164 = 8 + (k-1)6

156 = (k-1)6

156/6 =k-1

26 = k-1

K = 27

Answer 2

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