SOLUTION: An ap consists 25 terms, of which 4th term is 4 and 22nd term is 5.what would be the 19th term?

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Question 1118234: An ap consists 25 terms, of which 4th term is 4 and 22nd term is 5.what would be the 19th term?
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39617) About Me  (Show Source):
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If common difference d, then from index 4 to index 22 is 22-4=18 of these d.

Term at index 4 is 4.
4%2B18d=5
18d=1
d=1%2F18

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The general term of the progression is 4%2Bd%2A%28n-1%29 for common difference d and index n.

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Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


I always encourage students to try working problems informally if at all possible. If you can do that, solving the problem by formal mathematical methods will make more sense.

Let's do a little mental arithmetic here to find the answer.

From the 4th term to the 22nd term is 18 terms; the difference between the 4th term and 22nd term is 1. So the common difference between terms has to be 1/18.

The 19th term is 3 terms before the 22nd term, which is 5: 5 - 3(1/18) = 5 - 3/18 = 5 - 1/6 = 4 5/6 or 29/6.