SOLUTION: Find the nth term of the harmonic sequence 1,4/5,2/3,4/7,... n=12

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Question 983172: Find the nth term of the harmonic sequence
1,4/5,2/3,4/7,... n=12
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

First find a formula for the general term.

1,4%2F5,2%2F3,4%2F7,... n=12
you can write first term 1 as 4%2F4 and third term 2%2F3 as 2%2F6, so your sequence will be:
4%2F4,4%2F5,4%2F6,4%2F7


in your case, numerators are same and equal to 4
as denominators, you have 4%7D%7D%2C+%7B%7B%7B5, 6, 7,...
to get first term
4%2F%28n%2Bd%29=1 where n=1 you have 4%2F%281%2Bd%29=1=> d must be equal to 3
4%2F%281%2B3%29=1=>4%2F4=1
so, general formula will be:
a%5Bn%5D=+4%2F%28n%2B3%29 (for all terms given) where n=1,2,3,.....n
a%5Bn+%5D=+4%2F%28n%2B3%29 ...........if n=12 we have
a%5B12+%5D=+4%2F%2812%2B3%29
a%5B12+%5D=+4%2F15