SOLUTION: The 2nd term of an A.P is (a-b) and 4th term is (a+b), find the 5th term and sum of the first 5 terms of the A.P

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Question 1008007: The 2nd term of an A.P is (a-b) and 4th term is (a+b), find the 5th term and sum of the first 5 terms of the A.P
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
d, common difference
index 2, term is a-b
index 4, term is a+b

%28a%2Bb%29-%28a-b%29=2d
2b=2d
highlight_green%28b=d%29

The term at index 1 is %28a-b%29-d=%28a-b%29-b=a-b-b=highlight_green%28a-2b%29.
The general term for the sequence using n for iNdex is highlight%28%28a-2b%29%2B%28n-1%29b%29.

The term at index 5?
a-2b%2B%285-1%29b
a-2b%2B4b
highlight%28a%2B2b%29

You can look for the formula for sum of an arithmetic sequence to answer sum of the
first five terms. You might also just use this:
highlight_green%28%28firstTerm%2BlastTerm%29%28n%2F2%29%29, and you know n=5 here.