Question

If 'l' is the last term of A.P. say the nth term, the sum of all terms of A.P. is will be given by​

Answer 1

Step-by-step explanation:

General formula for sum of an AP

= 2n×(2a+(n−1)d)

= 2n×(a+a+(n−1)d)

= 2n×(a+l), where l is the last term

Answer 2

Answer:

If 'l' is the last term of A.P., say the nth term, the sum of all terms of A.P. will be given by

$n^{th} \ term \ of \ an \ AP ,a_n=a+(n-1)d=l \ [given] \\\\ sum \ of \ all \ terms \ i.e.,n \ terms \ is \ given \ by, \\\\ S_n=\frac{n}{2} [2a+(n-1)d] \\\\ S_n=\frac{n}{2} [a+a+(n-1)d] \\\\ S_n=\frac{n}{2} [a+l]$