3.39: AP first term, common difference and SnS_n identity

0606/23/O/N/21 — Question 9 · 12 marks

(a)
An AP has third term 1313 and tenth term 4141. Find aa and dd.
[4]
(b)
Find the number of terms required to give a sum of 25552555.
[4]
(c)
Given that SnS_{n} is the sum to nn terms, show that S2k−Sk=3k(2k+1)S_{2k}-S_{k}=3k(2k+1).
[4]