For the harmonic sequences given below, how to find the indicated term?
(1) #1/10# , #1/6# , #1/2# ,....; 9th term
(2) #1/15# , #1/13# , #1/11# ,....; 9th term
(3) #1/4# ,#1/14# , #1/24# ,....; 6th term
(1)
(2)
(3)
1 Answer
Jul 8, 2018
Explanation:
A harmonic sequence is the reciprocal of an arithmetic sequence:
Notice the denominators in each sequence:
(1)
Common difference:
First term:
The nth term of an arithmetic sequence is given by:
So for the 9th term we have:
And for the harmonic sequence:
We can do the same thing for 2 and 3:
(2)
(3)