Question

The sum of the first 9 of an AP is 72 and the sum is next 3 terms is 71 find the AP

Answer 1

what do you know? If I can figure what you meant,

9/2 (2a+8d) = 72
12/2 (2a+11d) = 72 + 71
Now just solve for a and d, and you can write the AP

Answer 2

Trying to make sense of your typing:

Do you mean:
The sum of the first 9 terms of an AP is 72 and the sum of the next 3 terms is 71 ....

If so, then -----

(9/2)(2a + 8d) = 72
9(a + 4d) = 72
a + 4d = 8 , #1

a+9d + a+10d + a+11d = 71
3a + 30d = 71 , #2
multiply #1 by 3
3a + 12d = 24 , subtract this from #2

18d = 47
d = 47/18
in #1, a + 4(47/18) = 8
a = -22/9

the AP is
-22/9, 1/6, 25/9, 97/18, ....

sum(9) = (9/2)(2(-22/9) + 8(47/18) ) = 72
sum(12) = 6(2(-22/9) + 11(47/18) ) = 143
so the sum of the last 3 terms must be 143-72 = 71

My answer is correct