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Question
Find the next 4 terms of the sequence `1/6, 1/4, 1/3`. Also find Sn.
Solution
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 = ((6 - 4)/(6 xx 4))= 2/24 = 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`
Sn = `"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)`
∴ Sn = `("n"("n" + 3))/24`
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