1.18: The sum of the first 10 terms of an arithmetic series is where is a constant.

4PM1/1R/June/2024 — Question 5 · 11 marks

The sum of the first 10 terms of an arithmetic series A\displaystyle A is 36k+1\displaystyle 36k + 1 where k\displaystyle k is a constant.
The 6th term of A\displaystyle A is 4k+1\displaystyle 4k + 1
(a) (i) Find an expression in terms of k\displaystyle k for the common difference of A\displaystyle A
(ii) Show that the first term of A\displaystyle A is −8\displaystyle -8
(5)
Given that the 4th term of A\displaystyle A is 7
(b) show that k=4\displaystyle k = 4
(2)
The sum of the first n\displaystyle n terms of A\displaystyle A is Sn\displaystyle S_n and the n\displaystyle nth term of A\displaystyle A is Un\displaystyle U_n
(c) Find the value of n\displaystyle n such that Sn=5Un+10+105\displaystyle S_n = 5U_{n+10} + 105
(4)