1.15: Past-paper question 8

4PM1/2/November/2023 — Question 8 · 10 marks

The sum to n\displaystyle n terms of an arithmetic series A\displaystyle A is Sn\displaystyle S_n
The sum of the first four terms of A\displaystyle A is 42 and the fifth term of A\displaystyle A is 23
(a) Show that Sn=∑r=1n(Pr−Q)\displaystyle S_n = \sum_{r=1}^n (Pr - Q) where P\displaystyle P and Q\displaystyle Q are prime numbers.
(6)
S2n−3Un=1062\displaystyle S_{2n} - 3U_n = 1062 where Un\displaystyle U_n is the n\displaystyle nth term of A\displaystyle A
(b) Find the value of n\displaystyle n
(4)