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

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

Problem

Which of the following 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[2a+nd\bigr]

(b)

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

(c)

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

(d)

S_n=n\bigl[2a+(n-1)d\bigr]