Given: S8 = 64 and S19 = 361
We know that,
⇒ 38 = 2a + 18d …(ii)
Solving linear equations (i) and (ii), we get
2a + 7d – 2a – 18d = 16 – 38
⇒ -11d = -22
⇒ d = 2 …(iii)
Putting the value of d in eq. (i), we get
2a + 7(2) = 16
⇒ 2a = 16 – 14
⇒ 2a = 2 …(iv)
Now, we have to find the Sn
[from (iii) and (iv)]
⇒ Sn = n [1 + n – 1]
⇒ Sn = n2