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the sum of three consecutive terms of an ap is 21 and the sum of the squares of these terms is 165. Find the terms.​

Answer»

Question : The sum of three CONSECUTIVE TERMS of an ap is 21 and the sum of the SQUARES of these terms is 165. Find the terms

Step-by-step explanation:

Let 1st consecutive term =   a-d

Let 1st consecutive term =   a-dLet 2nd consecutive term =  a

Let 1st consecutive term =   a-dLet 2nd consecutive term =  aLet 3rd consecutive term = a+d

Here , you can conclude that d is the  common difference

so ,

ACCORDING To problem:  

a-d + a+ a-d =21

3a= 21

a=7

Now let's square them all :

(a-d)²+a²+(a+d)²=165

a²-2ad+d²+a²+a²+2ad+d²=165

3a²+2d²=165

147+2d²=165

2d²=18

d²=9

d=3

Now put the values :

a - d = 7 - 3

a-d =  4

a + d = 7 + 3

a+d = 10

Hence , The terms are 4,7,10


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