Question

If the sum of three consecutive terms of an increasing A.P. is 51 and theproduct of first and third terms is 273, find the third term

Answer 1

Let 3 consecutive terms A.P is a –d, a , a + d. and the sum is 51

so, (a –d) + a + (a + d) = 51
> 3a –d + d = 51
> 3a = 51
> a = 17

The product of first and third terms is 273

So  it stand for ( a –d) (a + d) = 273
 >a 2 –d 2 = 273
> 172 –d 2 = 273
>  289 –d 2 = 273
>  d 2 = 289 –273
>  d 2 = 16
>  d = (plus and minus) 4

so now put plus and minus eventually to get the third term. 

Answer 2

Answer: Correct answer is 21