Question

if a , d ,l be the first term , common difference and last term of an AP respectively , find the number of terms in the AP

Answer 1

n=(l-a)/d + 1
Hope it helps you.

Answer 2

Let
$a \: = the \: first \: term \\ d = common \: difference \\ a_{n} = l\: be \: the \: last \: term \\ n = no. \: of \: terms$

Therefore,
$a_{n} = l \\ = > a + (n - 1)d= l \\ = > (n - 1)d=l - a \\ = > (n - 1) = \frac{l - a}{d} \\ = > n = ( \frac{l - a}{d} ) + 1 \\ = > n = \frac{l - a + d}{d}$