SOLUTION: Which term of the series 79,77,75___ is 47.find out the an.

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Question 980165: Which term of the series 79,77,75___ is 47.find out the an.
Answer by MathLover1(20850) About Me  (Show Source):
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Which term of the series 79,77,75___ is 47.
find out the a%5Bn%5D
as you can see, the differences between each pair of numbers are always 2, each next term is 2 less then previous one
a+=+79 (the first term)
d+=+2 (the "common difference" between terms)
And we get:
{ a, a-d, a-2d, a-3d, ... }
We can write an arithmetic sequence as a rule:
a%5Bn%5D+=+a+-+d%28n-1%29
(We use "n-1" because d+is not used in the 1st term).
check the formula:
a%5B1%5D+=79+-+2%281-1%29=79
a%5B2%5D+=79+-+2%282-1%29=79+-+2%281%29=79-2=77
a%5B3%5D+=79+-+2%283-1%29=79+-+2%282%29=79-4=75
calculate which term is equal to 47:
47=+79+-+2%28n-1%29
47=+79+-+2n%2B2
47=+81+-+2n
2n=+81+-+47
2n=+34
n=+34%2F2
n=+17
so, 47 is 17th term
check:
79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,highlight%2847%29