Question

in ap 19th term is 52 and 38th term is 128 find the sum of first 56 term

Answer 1

T19 = 52
T38= 128
So , a+ 18d = 52 ...( 1 )
a+ 37d = 128... ( 2 )
(-)
- 19d= -76

d= 76/19
d= 4.

So , By (1)
a. = 52 - 18(4)
a = (-20)

So...

S(56) = 56/2[ 2(-20) + 55(4) ]
= 28 [ -40 + 220]
=28× 180
=5040.