Question

Geometric sequences HELP ASAP!

Answer 1

Given:

The table for a geometric sequence.

To find:

The formula for the given sequence and the 10th term of the sequence.

Solution:

In the given geometric sequence, the first term is 1120 and the common ratio is:

`r=(a_2)/(a_1)`

`r=(560)/(1120)`

`r=0.5`

The nth term of a geometric sequence is:

`a_n=ar^(n-1)`

Where a is the first term and r is the common ratio.

Putting
`a=1120, r=0.5`, we get

`a_n=1120(0.5)^(n-1)`

Therefore, the required formula for the given sequence is
`a_n=1120(0.5)^(n-1)`.

We need to find the 10th term of the given sequence. So, substituting
`n=10` in the above formula.

`a_(10)=1120(0.5)^(10-1)`

`a_(10)=1120(0.5)^(9)`

`a_(10)=1120(0.001953125)`

`a_(10)=2.1875`

Therefore, the 10th term of the given sequence is 2.1875.