Question

find and give explanation 24

Answer 1

Sn =n/2 (2a+n-1)d)
sum of first 7 terms =49
s7 =(2a+n-1)d)
49= 7/2 (2a+7-1)d)
49=7/2 (2a+6d)
49×2/7 = 2a+6d
14=2a+6d
14 - 6d =2a
14- 6d/2 = a
a=7-3d ....... (1)

sum of first 17 terms =289
S17 =17/2 (2a +17-1)d)
289=17/2 (2a+17-1)d)
289=17/2 (2a+16d)
289×2/17= 2a+16d
34=2a+16d
34 -1 6d =2a
34-16d/2 =a
a=17-8d .......... (2)


from 1 and 2
7-3d=17-8d
8d-3d=17-7
5d=10
d=10/5
d=2

putting value of d in 1
a=7-3d
a=7- 3×2
a=7-6
a=1

hence a=1 , d=2