Which of the following correctly gives the sum of the first terms of an arithmetic…

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

Problem

Which of the following correctly gives the sum

S_n

of the first

n

terms of an arithmetic progression whose first term is

a

and common difference is

d

? (a)

S_n = \dfrac{n}{2}\bigl(a + (n-1)d\bigr)

(b)

S_n = \dfrac{n}{2}\bigl(2a + (n-1)d\bigr)

(c)

S_n = a + (n-1)d

(d)

S_n = \dfrac{n}{2}\bigl(2a + nd\bigr)