In an A.P. If the 5th and 12th terms are 30 and 65 respectively, what is the sum of first 20 terms?
According to question,
a5= 30
a + 4d = 30
a = 30 – 4d (i)
a12= 65
a + 11d = 65
30 – 4d + 11d = 65 [from (i)]
7d = 35
d = 5
Put d in (i)
a = 30 – 4(5)
= 10
S20= 
[2(a) + (20 – 1) d]
= 10 [2(10) + 19(5)]
= 10 {20 + 95}
= 1150
20