The arithmetic progression has first term 2 and common difference 3.

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

Problem

The arithmetic progression has first term 2 and common difference 3. (i) Form the equation satisfied by

n

if the

n

th term of the progression equals

n^{2}-2n+5

. (ii) Solve the equation obtained in part (i) to find all positive integral values of

n

that satisfy it. (iii) Write down the term (or terms) of the progression corresponding to the value(s) of

n

found in part (ii). (iv) Compute the sum of all terms of the progression up to and including the largest of these terms.