SOLUTION: The first difference of a sequence is 3, 9, 15, 21,... The sum of the first two terms of the original sequence is 21. Find the first three terms of the original sequence.

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Question 933534: The first difference of a sequence is 3, 9, 15, 21,... The sum of the first two terms of the original sequence is 21. Find the first three terms of the original sequence.
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
a%5B2%5D-a%5B1%5D=3, a%5B3%5D-a%5B2%5D=9, a%5B4%5D-a%5B3%5D=15, a%5B5%5D-a%5B4%5D=21,
3, 9, 15, 21
Since we are given that
a%5B2%5D%2Ba%5B1%5D=21, we have the system
system%28a%5B2%5D-a%5B1%5D=3%2Ca%5B2%5D%2Ba%5B1%5D=21%29
Solve that system and get a%5B2%5D=12 and a%5B1%5D=9, so
a%5B3%5D-a%5B2%5D=9
a%5B3%5D-12=9
a%5B3%5D=21
a%5B4%5D-a%5B3%5D=15,
a%5B4%5D-a%5B3%5D=15
a%5B4%5D-21=15
a%5B4%5D=36
a%5B5%5D-a%5B4%5D=21,
a%5B5%5D-36=21
a%5B5%5D=57
The general term, BTW, is 3%28n%5E2-2n%2B4%29
Edwin