SOLUTION: An arithmetic progression has 241 terms and a common difference of 0.1 given the sum of the terms is 964. Find the first term.

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Question 1016780: An arithmetic progression has 241 terms and
a common difference of 0.1 given the sum of
the terms is 964. Find the first term.

Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
An arithmetic progression has 241 terms and a
common difference of 0.1 given the sum of the
terms is 964. Find the first term.

S%5Bn%5D%22%22=%22%22expr%28n%2F2%29%282a%5B1%5D%2B%28n-1%29d%5E%22%22%29

Substitute n=241 and d=0.1

S%5B241%5D%22%22=%22%22expr%28241%2F2%29%282a%5B1%5D%2B%28241-1%29%280.1%29%5E%22%22%29

And substitute S241 = 964

964%22%22=%22%22expr%28241%2F2%29%282a%5B1%5D%2B%28241-1%29%280.1%29%5E%22%22%29

964%22%22=%22%22expr%28241%2F2%29%282a%5B1%5D%2B%28240%29%280.1%29%5E%22%22%29

964%22%22=%22%22expr%28241%2F2%29%282a%5B1%5D%2B24%5E%22%22%29

Clear the fraction by multiplying both sides by 2

1928%22%22=%22%22241%282a%5B1%5D%2B24%5E%22%22%29

Divide both sides by 241

8%22%22=%22%222a%5B1%5D%2B24

Subtract 24 from both sides

-16%22%22=%22%222a%5B1%5D

Divide both sides by 2

-8%22%22=%22%22a%5B1%5D

First term is -8

Edwin