IAL 2026 Jan FP1 Q8

Question

[!problem]

(a) Use the standard results for summations to show that

$\sum_{r=1}^{n} (2r - 1)^3 = An^2 + B$

where $A$ and $B$ are integers to be determined.

(5)

(b) Use the answer to part (a) to determine the value of

$25^2 + 27^2 + 29^2 + \cdots + 95^2$

You must make your method clear.

(3)