Q. If the first, second and last terms of an arithmetic series are $a,b$ and $c$ respectively, then the number of terms is
A) $\frac{b + c - 2a}{b - a}$
B) $\frac{b + c + 2a}{b - a}$
C) $\frac{b + c - 2a}{b + a}$
D) $\frac{b + c + 2a}{b + a}$
Explanation
(a)
Since, $l = A + (n - 1)d$
$\therefore c = a + (n - 1)(b - a)$
$\Rightarrow (n - 1) = \frac{c - a}{b - a}$
$\Rightarrow n = \frac{b + c - 2a}{b - a}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.