# math

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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 -

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!

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