Question

If the 12 th term of ap is -13 and the sum of first 4 term is 24 . What is the sum of first 20 terms

Answer 1

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Answer 2

let a is the first and d is the common difference of AP

a/c to question ,
12th term = -13
use nth term formula ,
Tn=a +(n-1) d
so,
a +(12 -1) d = -13
a + 11 d = -13 ----------(1)

again ,
sum of 1st 4 terms =24

use,
Sn =n/2 {2a+(n-1) d}
so,
4/2 {2a + (4 -1) d } =24
2 a + 3d = 12 -------------(2)

solve equation (1) and (2)
2 x (1) - (2)

2 a + 22d - 2a -3d = -26 -12
19d = -38
d = - 2
put d = -2 in equation (1)
a = -13 +22
=9

now,
sum of 20 terms =20/2 { 2.9 + (20 -1)(-2)}
= 10 (18-38)= -200