SOLUTION: first term a, common difference d the sum of the first 200 terms is 4 times the sum of the first 100 terms -find d in terms of a -find the 100th term in terms of a

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Question 933070: first term a, common difference d
the sum of the first 200 terms is 4 times the sum of the first 100 terms
-find d in terms of a
-find the 100th term in terms of a
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
The sum of the first n terms is
%282a%2B%28n-1%29%2Ad%29%28n%2F2%29 , so
the sum of the first 200 terms is
%282a%2B%28200-1%29d%29%28200%2F2%29=%282a%2B199d%29%28100%29=200a%2B19900d , and
the sum of the first n terms is
%282a%2B%28100-1%29d%29%28100%2F2%29=%282a%2B99d%29%2850%29=100a%2B4950d .
Since the sum of the first 200 terms is 4 times the sum of the first 100 terms,
200a%2B19900d=4%28100a%2B4950d%29
200a%2B19900d=400a%2B19800d
100d=200a
d=200a%2F100
highlight%28d=2a%29
The n%5Eth therm is a%2B%28n-1%29%2Ad , so the 100%5Eth term is
a%2B%28n-1%29%2A%282a%29=a%281%2B%28n-1%29%2A2%29=a%281%2B2n-2%29=highlight%28a%282n-1%29%29 .