If n term of an AP is (3n+7), then find the sum of first 20 terms.

1 answer

an = 3 n + 7

n = 1

a1 = 3 ∙ 1 + 7 = 3 + 7 = 10

n = 2

a2 = 3 ∙ 2 + 7 = 6 + 7 = 13

13 - 10 = 3

n = 3

a3 = 3 ∙ 3 + 7 = 9 + 7 = 16

16 - 13 = 3

etc.

This is AP where first term is a1 = 10 and common difference d = 3

In AP:

an = a1 + ( n - 1 ) d

a20 = a1 + 19 d

a20 = 10 + 19 ∙ 3 = 10 + 57

a20 = 67

Sum on n term in AP:

Sn = n ( a1 + an ) / 2

In this case n = 20:

S20 = 20 ( a1 + a20 ) / 2

S20 = 20 ( 10 + 67 ) / 2 = 20 ∙ 77 / 2 = 770