Math
posted by Anonymous on .
The sum of 16terms oe an A.P is 504,while the sum of its 9terms is 126.Find the sum of its 30terms

sum of 16 terms is 504 > 8(2a + 15d) = 504
2a + 15d = 63
sum of 9 terms is 126 > (9/2)(2a + 8d) = 126
2a + 8d = 28
subtract:
7d = 35
d=5
in 2a+8d=28
2a  40 = 28
2a = 12
a=6
sum(30) = 15(12 + 29(5)) = 1995 
S_{16} = 16/2 * (2a+15d) = 504
S_{9} = 9/2 * (2a + 8d) = 126
16a + 120d = 504
9a + 36d = 126
Multiply #1 by 9 and #2 by 16, then subtract:
144a + 1080d = 4536
144a + 576d = 2016
504d = 2520
d = 5
a = 6
S_{30} = 15(2a+29d) = 15(12  145) = 1995 
1995