Question
find the n th term of the series 5/2+20/13+10/9+20/23..... .
Answers
Reiny
Just like in your previous problem, the corresponding AS is
2/5 + 13/20 + 9/10 + 23/20 + ...
= 8/20 + 13/20 + 18/20 + 23/20 + ...
looks like a = 8/20, and d = 5/20
or a = 2/5 and d = 1/4
so term(n) of this AS
= a + (n-1)d
= 2/5 +(1/4)(n-1)
= 2/5 + n/4 - 1/4
= n/4 + 3/20
= (5n + 3)/20
and finally the general term of the given HS
= 20/(5n+3)
2/5 + 13/20 + 9/10 + 23/20 + ...
= 8/20 + 13/20 + 18/20 + 23/20 + ...
looks like a = 8/20, and d = 5/20
or a = 2/5 and d = 1/4
so term(n) of this AS
= a + (n-1)d
= 2/5 +(1/4)(n-1)
= 2/5 + n/4 - 1/4
= n/4 + 3/20
= (5n + 3)/20
and finally the general term of the given HS
= 20/(5n+3)
Pranitha
20/5n+3