Question

In an ap if sum of its first n terms is 3 and square + 5 and its kit term is 164 then find the value of k

Answer 1

S = 3n2 + 5n

S1 = a1 = 3 + 5 = 8

S2 = a1 + a2

= 12 + 10 = 22

⇒ a2 = S2 - S1

= 22 - 8 = 14

S3 = a1 + a2 + a3

= 27 + 15 = 42

⇒a3 = S3 - S2

= 42 - 22 = 20

∴ Given AP is 8,14,20.....

Thus a = 8 , d = 6

Given tm = 164. 164

= [a + (n -1)d] 164

= [(8) + (m -1)6] 164

= [8 + 6m - 6] 164

= [2 + 6m] 162

∴ m = 27