SOLUTION: What is the product of the 6th term and the reciprocal of the 7th term of the sequence 1/10,3/20.1/5.1/4.3/10,_,_

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Question 1136759: What is the product of the 6th term and the reciprocal of the 7th term of the sequence
1/10,3/20.1/5.1/4.3/10,_,_
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

1%2F10,3%2F20.1%2F5.1%2F4.3%2F10,_,_
The formula for nth term of an arithmetic progression is
a%5Bn%5D=a%5B1%5D%2B%28n-1%29d.
In this example we have d=3%2F20-1%2F10=3%2F20-2%2F20=1%2F20 and a%5B1%5D=1%2F10 so.
6th term, n=6
a%5B6%5D=1%2F10%2B%286-1%29%281%2F20%29
a%5B6%5D=1%2F10%2B5%2F20
a%5B6%5D=2%2F20%2B5%2F20
a%5B6%5D=7%2F20
7th term, n=7
a%5B7%5D=1%2F10%2B%287-1%29%281%2F20%29
a%5B7%5D=1%2F10%2B6%2F20
a%5B7%5D=2%2F20%2B6%2F20
a%5B7%5D=8%2F20
a%5B7%5D=2%2F5
the product of the 6th term and the reciprocal of the 7th term is:
the reciprocal of the 7th term is 5%2F2
and a%5B6%5D%281%2Fa%5B7%5D%29=%287%2F20%29%285%2F2%29=35%2F40=7%2F8