For an arithmetic progression with first term and common difference

MATHEMATICS · Single correct · CBSE · Mathematics · Arithmetic Progressions · Arithmetic Progressions

Problem

For an arithmetic progression with first term

a

and common difference

d

, let

T_n=a_1+a_3+a_5+\dots+a_{2n-1}

be the sum of the first

n

odd-indexed terms. Which expression represents

T_n

? (a)

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

(b)

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

(c)

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

(d)

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