# HOW TO FIND THE SUM OF GIVEN NUMBER OF TERMS FROM INDICATED TERMS

How to Find the Sum of Given Number of Terms from Indicated Terms ?

By using the formula for an, we may form equations and solve for the variables "a" and "d".

To find the sum of n terms of an arithmetic progression, we may use one of the formulas given below.

Sn  =  (n/2) [a + l] (or)

Sn  =  (n/2) [2a + (n - 1)d]

a = first term, d = common difference and n = number of terms.

To find the indicated term, we may use the formula for an.

a=  a + (n - 1)d

## How to Find the Sum of Given Number of Terms from Indicated Terms - Examples

Question 1 :

Find the sum of first 22 terms of an AP in which d = 7 and 22nd term is 149.

Solution :

n  =  22, d  =  7

a22  =  a + 21d  =  149  ----(1)

By applying the value of d in (1), we get

a + 21(7)  =  149

a + 147  =  149

a  =  149 - 147

a  =  2

Now, we have to find sum of 22 terms.

Sn  =  (n/2) [2a + (n - 1)d]

=  (22/2) [2(2) + (22 - 1)7]

=  11 [4 + 21(7)]

=  11 [4 + 147]

=  11 (151)

=  1661

Question 2 :

The sum of first 51 terms of an AP whose second and third terms are 14 and 18 respectively.

Solution :

Given that :

Second term (a2)  =  14

a + d  =  14 -----(1)

Third term (a3)  =  18

a + 2d  =  18 -----(2)

(1) - (2)

(a + d) - (a + 2d)  =  14 - 18

d - 2d  =  -4

-d  =  -4

d  =  4

By applying the value of d in (1), we will get "a".

a + 4  =  14

a  =  14 - 4  =  10

Now, we have to find the sum of 51 terms.

Sn  =  (n/2) [2a + (n - 1)d]

=  (51/2)[2(10) + (51 - 1)4]

=  (51/2) [ 20 + 200]

=  (51/2)(220)

=  5610

After having gone through the stuff given above, we hope that the students would have understood, how to find the sum of given number of terms from indicated terms.

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