Consider the arithmetic progression (A.P.) 7, 10, 13, …

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

Problem

Consider the arithmetic progression (A.P.) 7, 10, 13, … (i) State the formula for the sum of the first

n

terms of an A.P. (ii) Let

S_p

and

S_q

(q>p)

denote the sums of the first

p

and first

q

terms of an A.P. Explain, without using specific numbers, why the sum of the terms from the

(p+1)

th term to the

q

th term is

S_q-S_p

. (iii) Using the result of part (ii), find the sum of the terms from the 6th term to the 15th term (both inclusive) of the given A.P.