Question

The sum of three consecutive terms of an
increasing A.P. is 51. If the product of the first
and third of these terms be 273, then third term is.
(A) 13 (B) 17 (C)21 (D) 9

plz give answer with method
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Answer 1

3 consecutive no.=x-a,x and x+a

Given, x-a+x+x+a=51

3x=51 so x=17

Also, Given that product of 1st and 3rd no. is 273

I.e.(x-a)(x+a)=273

x²-a²=273

put x=17 we get,

a²=17²-273=289-273

a²=16

so a=4

so 3rd no.=x+a=17+4

=21.

Answer 2

Answer:

Let 1st term be a-d

2nd term a

3rd term a+d

Sum is 51

a-d + a +a+d =51

3a =51

a=17

Product of 1st & 3rd =273

a-d*a+d=273

17-d*17+d=273

289-d square=273

d square=16

d =4

Then 3rd term is a+d

17+4=21