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

Question 1 :

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

S_n  =  (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

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