Question

write the formula to find the sum of the first n term of an Ap, where first term is a and the last term is an​

Answer 1

Answer:

Formula to find sum of given n terms is

Sn=n/2[2a+(n-1)×d]

If last term is given then

Sn=n/2(a+l)

Answer 2

$S_{n}=\dfrac{n}{2}(a+a_{n})$

Step-by-step explanation:

Let the common difference be $d$

Given, first terms is $a$

Then, 2nd term is $a+d$

... ... ...

and nth term is $a+(n-1)d$

So, sum of these n-terms

$=a+(a+d)+...+[a+(n-1)d]$

$=(a+a+...n-times)+[1+2+...+(n-1)d]$

$=na+\dfrac{(n-1)[(n-1)+1]}{2}d$

$=\dfrac{1}{2}[2na+n(n-1)d]$

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

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

$=\dfrac{n}{2}(a+a_{n})$

#SPJ3