The sums of the first terms of an A.P

MATHEMATICS · Multi-part · A Level · Mathematics · Sequences and series · Sequences and series

Problem

The sums of the first

n

terms of an A.P. and a G.P. are equal. The A.P. has first term

5

and common difference

3

. The G.P. has first term

5

and positive common ratio

r

, where

r \neq 1

. (i) Obtain the equation involving

n

and

r

that follows from the equality of the two sums. (ii) Given further that

r

satisfies

r^2 + r - 2 = 0

, determine the admissible value of

r

. (iii) For the value of

r

found in part (ii), calculate the corresponding positive integer

n