1.20: Past-paper question 2

The sum of the fifth, sixth and seventh terms of an arithmetic series $\displaystyle A$ is nine times the sum of the first and second terms.

The third term of $\displaystyle A$ is 12

(a) Find the first term and common difference of $\displaystyle A$

The $\displaystyle n$th term of $\displaystyle A$ is $\displaystyle u_n$

(b) Find the value of $\displaystyle \sum_{r=15}^{60} u_r$

The sum to $\displaystyle n$ terms of $\displaystyle A$ is $\displaystyle S_n$

Given that $\displaystyle 2S_n - 5u_n = 10$

(c) find the value of $\displaystyle n$