If 1² + 2² + 3² + . . . . . + p² = $$\left[ {\frac{{{\text{p}}\left( {{\text{p}} + 1} \right)\left( {2{\text{p}} + 1} \right)}}{6}} \right]{\text{,}}$$     then 1² + 3² + 5² + . . . . . + 17² is = ?

A. 969

B. 1785

C. 980

D. 1700

Answer: Option A

Solution(By Examveda Team)

1² + 3² + 5² + . . . . . + 17²
= (1² + 2² + 3² + 4² + . . . . . + 17²) - (2² + 4² + . . . . . + 16²)
= (1² + 2² + 3² + 4² + . . . . . + 17²) - 2²(1² + 2² + . . . . . + 8²)
Using given formula
$$\eqalign{ & \left[ {\frac{{p\left( {p + 1} \right)\left( {2p + 1} \right)}}{6}} \right] \cr & = \frac{{17 \times 18 \times 35}}{6} - 4\left[ {\frac{{8 \times 9 \times 17}}{6}} \right] \cr & = 1785 - 4 \times 204 \cr & = 1785 - 816 \cr & = 969 \cr} $$