Sum of first n terms of A.P will be **n**^{2 }

**Explanation :**

n_{1}=7

S_{n}=49

we know that **S**_{n} = **n/2{2a+(n-1)d}**

thus,

S_{n}_{1}=7/2(2a+6d)=49

=14a+42d=98 ... (1) x17

n_{2}=17

Sn_{2}=289

Sn_{2}=17/2(2a+16d)=289

=34a+272d=578 ....(2) x7

from eq 1 & 2

238a +714d =1666 ....(3)

238a +1904d=4046 .....(4)

subtracting (4) -(3)

1190d=2380

d=2

a=1

sum of n terms will be **S**_{n} = **n/2{2a+(n-1)d}**

**S**_{n} = **n**^{2 }