Question

The sum of 15 th and 20 th terms of an AP is 80. Its 28th term is 60 , Find 7th term.

Answer 1

Step-by-step explanation:

Let a and d be the first term and the common difference of the AP.

Concept

If a and d are first term and common difference of an AP, then its nth term is given by

aₙ = a + (n-1)d

Equations

Sum of 15th and 20th term is 80, so

a₁₅ + a₂₀ = 80

or (a + 14d) + (a + 19d) = 80

or 2a + 33d = 80 ............(1)

28 th term of the AP is 60 , so

a₂₈ = 60

or a + 27d = 60 ..........(2)

Substracting (2) from (1) we get

(2a + 33d) - (a + 27d) = 80 - 60

or a + 6d = 20

or a₇ = 20

Therefore, seventh term of the AP is 20.