Question

In an ap 5th and 12th term are 30 and 65.find sum of first 20 terms

Answer 1

Hi !

a₅ = 30
a + 4d = 30 ----> (1)

a₁₂ = 65
a + 11d = 65 ----> [2]


solving equations 1 and 2 ,

(2) - (1)

a + 11d = 65
- a + 4d = 30
---------------------
7d = 35

d = 5

a + 4d = 30
a + 20 = 30

a = 30 - 20

a = 10

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sum of first 20 terms :-

a = 10
d = 5
n = 20

Sn = n/2 [ 2a + [ n-1]d ]
=20/2 [ 20 + 19 x 5]
= 10 [ 115]
= 1150

sum of first 20 terms = 1150