SOLUTION: Find the 100th term of 25, 10, -5, -20,...

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Question 978109: Find the 100th term of 25, 10, -5, -20,...
Found 2 solutions by Boreal, MathLover1:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
Each term is 15 less than the previous.
The 100th term is 1485 [(100-1)*15] less than the first term or -1460.
It is the first term, 25 + (100-1) difference or 25 + 99(-15)=-1460
The 100th term is -1460.

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

25, 10, -5, -20,...
This is an arithmetic progression (AP).
The n-th term of an AP with first term 'a%5B1%5D' and common difference 'd' is
a%5Bn%5D=a%5B1%5D%2B%28n-1%29d

in your case, a%5B1%5D+=+25 and d+=10-25=+-15
So the 100-th term is:
a%5B100%5D=25%2B%28100-1%29%28-15%29
a%5B100%5D=25%2B%2899%29%28-15%29
a%5B100%5D=25-1485
a%5B100%5D=-1460