In the formula for an arithmetic progression

MATHEMATICS · Single correct · A Level · Mathematics · Sequences and series · Sequences and series

Problem

In the formula

S_n = \dfrac{n}{2}[2a + (n - 1)d]

for an arithmetic progression, what does the quantity inside the brackets

[\,2a + (n - 1)d\,]

represent? (a) Twice the

n^{\text{th}}

term (b) Twice the first term (c) The sum of the first and

n^{\text{th}}

terms (d) The difference between the first and

n^{\text{th}}

terms