The first, third and fourth terms of a sequence are given as , and…

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

Problem

The first, third and fourth terms of a sequence are given as

2y - 1

y + 1

and

4y - 2

respectively. (i) Show that the sequence can be an arithmetic progression only for specific value(s) of

y

and find that value. (ii) Using the value of

y

obtained, write the first five terms of the progression. (iii) Find the sum of the first 25 terms.