Question

In an arithmetic​ sequence, the nth term an is given by the formula an=a1+(n−1)d​, where a1 is the first term and d is the common difference.​ Similarly, in a geometric​ sequence, the nth term is given by 1an=a1•rn−1​, where r is the common ratio. Use these formulas to determine the indicated term in the given sequence.

The 10th term of 40,10, 5/2, 5/8, ....

Answer 1

The 10th term of given sequence is
`(5)/(32768)`.

Explanation:

The given sequence is

`40,10, (5)/(2), (5)/(8), ....`

The given sequence is a geometric​ sequence because it have common ratio.

`r=(10)/(40)=((5)/(2))/(10)=((5)/(8))/((5)/(2))=(1)/(4)`

In the given sequence the first term of the sequence is 40.

`a_1=40`

The nth term of a GP is

`a_n=a_1r^(n-1)`

where,
`a_1` is first term and r is common ratio.

Substitute
`a_1=40` and
`r=(1)/(4)` in the above formula.

`a_n=40((1)/(4))^(n-1)`

Substitute n=10 , to find the 10th term.

`a_(10)=40((1)/(4))^(10-1)`

`a_(10)=(5)/(32768)`

Therefore the 10th term of given sequence is
`(5)/(32768)`.