Question

Find the next 4 terms of the sequence `1/6, 1/4, 1/3`. Also find S_n 

Answer 1

The given sequence is `1/6, 1/4, 1/3`

The above sequence is an A.P.

∴ a = `1/6`, d = `1/4 -1/6` = `(3 - 2)/12 = 1/12`

The next four terms of the sequence are

t₄ = t₃ + d = `1/3 + 1/12 = 5/12`

t₅ = t₄ + d = `5/12 + 1/12 = 6/12 = 1/2`

t₆ = t₅ + d = `1/2 + 1/12 = 7/12`

t₇ = t₆ + d = `7/12 + 1/12 = 8/12 = 2/3`

S_n = `"n"/2 [2"a" + ("n" - 1)"d"]`

= `"n"/2 [2(1/6) + ("n" - 1)(1/12)]`

= `"n"/2 (1/3 + 1/12 "n" - 1/12)`

= `"n"/2("n"/12 + 1/4)`

∴ S_n = `("n"("n" + 3))/24`