Question

9. If the sum of first 7 terms of an A.P is 49 and that of 17
terms is 289, find the sum of first n terms.​

Answer 1

Answer:

Step-by-step explanation:

S7=49

S17=289

=> S7=n/2{2a+(n-1)d}

-» 49=7/2[2a+(7-1)d]

49*2/7=(2a+6d)

14=2(a+3d)

7=a+3d-» a=7-3d —— (1)

S17=17/2[2a+(17-1)d]

289*2/17= 2a+16d

34= 2(7-3d)+16d —[from(1)]

34= 14-6d+16d

34-14=10d

d=20/10= 2

Putting value of d in eq. 1

a=7-3*2=1

Sn=n/2[2a+(n-1)d]

Sn= n/2[2*1+(n-1)2]

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

Sn n/2(2n)

Sn = n^2

Thank you

Hope it helps