Question

If the nth term of an A.P. is (7 – 3n), find the sum of first n terms of the A.P

Answer 1

an=7-3n
then first term, a=7-3=4
then
Sn=(n/2)(a+an)
=(n/2)(4+7-3n)
=(n/2)(11-3n)

Answer 2

Answer: $\frac{n}{2}(11-3n)$  

Concept: This is the question from 'Arithmetic Progression(A.P.), In A.P. difference between two consecutive terms will always be the same. To find the general term for AP we use the below formula

$a_{n}$= $a+(n-1)d$,

Given: $n^{th}$ term of AP=(7-3n)

To find the Sum of the first n terms of given A.P.

Solution:

here $n^{th}$ the term is given, we will get the first term of AP by put n=1 in

$n^{th}$ term= (7-3n)

First-term a= (7-3×1)

               a = 4

now we will find the sum of the given AP by using the below formula

   $S_{n}$=$\frac{n}{2} (a+a_{n})$

now put the values $a=4$ $&$& $a_{n} = (7-3n)$

$S_{n}$= $\frac{n}{2}( 4+7-3n)$

   $= \frac{n}{2} (11-3n)$

Hence the sum of the first n terms of the given AP is $\frac{n}{2}(11-3n)$