Discussion

Explanation:

S_n = n² + 2n

T_n = S_n – S_n-1

∴ T_n = (n² + 2n) - ((n – 1)² + 2(n – 1)) = 2n + 1

Sum of square of n terms = Σ(2n + 1)²

= Σ(4n² + 2n + 1)

= 4Σn² + 4Σn + Σ1

= 4$\left(\frac{n(n+1)(2n+1)}{6}\right)$ + 4$\left(\frac{n(n+1)}{2}\right)$ + n

∴ Sum of square of 10 terms = 4$\left(\frac{10(10+1)(20+1)}{6}\right)$ + 4$\left(\frac{10(10+1)}{2}\right)$ + 10

= 1540 + 220 + 10 = 1770.

Hence, 1770.

» Your doubt will be displayed only after approval.