Posted by Ahmad on Friday, October 28, 2011 at 5:40am.
The sum of the firest 9 terms of an A.P is 72 and the sum of the next 9 terms is 71, find the A.P

math  Reiny, Friday, October 28, 2011 at 9:42am
so the sum of 9 is 72 and
the sum of 18 = 72+71=143
(9/2)(2a + 8d) = 72 > 2a+8d=16
(18/2)(2a + 17d) = 143 > 2a + 17d = 143/9
subtract them
9d = 1/9
in 2a + 8d = 16
2a 8/9 = 16
2a = 152/9
a= 76/9
AP is 76/9 , 75/9, 74/9 ....
check for sum of 9 terms
first = 76/9
last = 76/9 + 8(1/9) = 68/9
sum(9) = (first+last)(9/2) = (76/9+68/9)(9/2) = 72
looking good!