The sum of the first terms of a sequence is S_n = pn^2 - 2n

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

Problem

The sum of the first

n

terms of a sequence is

S_n = pn^2 - 2n,

where

p

is a constant. It is known that the fifth term is

34

and the tenth term is

74

. (i) Express the

n

th term

a_n

in terms of

n

and

p

. (ii) Using the given information, find the value of

p

. (iii) Hence obtain the first term and the common difference of the sequence. (iv) Find the sum of the first 20 terms.