Question

the sum of first 7 term of AP is 119 and that of first 17th term is 714 find the sum of its first and terms

Answer 1

let first term be a and common diffrence be d

now, S7 = 7/2(2a+(7-1)d)

119 = 7/2(2a+6d)

119 = 7/2*2(a+3d)

119/7 = a+3d

17=a+3d .........................(1)



Also, S17 = 17/2(2a+(17-1)d

714 = 17/2*2(a+8d)

714/17 = a+8d

42 = a+8d ..........................(2)

Subtracting (1) from (2)

42-17 = a+3d-a-8d

25 = -5d

-5 = d

putting d= -5 in (1)

17 = a+ 3(-5)

17 = a-15

17+15 = a

32 = a

Now, a= 32 , d= -5

Sn = n/2(2<32>+ <n-1>-5)

Sn = n/2(64-5n+5)

Sn = n/2(69-5n)

Sn = 69n/2 - 5n2/2