Question

First term and the common differences of an A.P. are 6 and 3 respectively; find S₂₇.

Solution: First term = a = 6, common difference = d = 3, S₂₇ = ?

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

S_n = `27/2 [12 + (27 - 1)square]`

= `27/2 xx square`

= 27 × 45

S₂₇ = `square`

Answer 1

It is given that,

First term (a) = 6

Common difference (d) = 3 

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

∴ S₂₇ = `27/2 [2(6) + (27 - 1)bb((3))]`

= `27/2 (12 + 26 (3))`

= `27/2 (12 + 78)`

= `27/2 xx bb90`

= 1215

Hence, S₂₇ = 1215.