Question

if the sum of first 7 terms of an ap is 49 and that of 17 terms is 289 find the sum of first n terms​

Answer 1

Answer:

Step-by-step explanation:

Let a be the first term and d be the common difference

We have,

S7=49

7/2[2a+(7-1)d]=49

2a+(7-1)d=49×2/7

2a+6d=14 eq (1)

And

s17=289

17/2[2a+(17-1)d]=289

2a+16d=289×2/17

2a+16d=34 eq.(2)

Subtracting (1) from (2)

2a+16d-2a-6d=34-14

10d=20

d=2

Putting d=2 in (1)

2a+6(2)=14

2a+12=14

2a=14-12=2

a=1

now,

Sum of n terms

=n/2[2×1+(n-1)×2]

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

=n/2×2n

=n² (and)

Answer 2

Refers to attachment ♡♡~