Question

the sum of first 15 terms of an ap is 465 and the sum of first 14 terms of ap is 406 then it's 15th term is​

Answer 1

Given :- The sum of first 15 terms of an arithmetic progression is 465 and the sum of first 14 terms of the same arithmetic progression is 406. Then its 15th term is ?

Solution :-

Let us assume that, the terms in AP series are A1, A2, A3, ______A15 .

so,

→ A1 + A2 + A3 + __________ + A15 = 465 ------ Eqn.(1)

and,

→ A1 + A2 + A3 + ___________ A14 = 406 ------ Eqn.(2)

so, subtracting Eqn.(2) from Eqn.(1)

→ (A1 + A2 + A3 + __________ + A15) - (A1 + A2 + A3 + ___________ A14) = 465 - 406

→ (A1 - A1) + (A2 - A2) + __________ (A14 - A14) + A15 = 59

then,

A15 = 59 (Ans.)

Or,

→ S(15) - S(14) = A(15)

→ 465 - 406 = 59 (Ans.)