page 08 MARKS 14. A geometric sequence has first term 80 and common ratio 1 3 . (a) For this sequence, calculate: (i) the 7th term; (ii) the sum to infinity of the associated geometric series. The first term of this geometric sequence is equal to the first term of an arithmetic sequence. The sum of the first five terms of this arithmetic sequence is 240. (b) (i) Find the common difference of this sequence. (ii) Write down and simplify an expression for the nth term. Let Sn represent the sum of the first n terms of this arithmetic sequence. (c) Find the values of n for which n S = 144. 15. (a) Use integration by parts to find sin x x dx ∫ 3 . (b) Hence find the particular solution of sin , dy y x x x dx x − = ≠ 3 2 3 0 given that x = π when y = 0. Express your answer in the form ( ) y f x = . 2 2 2 1 3 3 7