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:

$r=\dfrac{a_2}{a_1}$

$r=\dfrac{560}{1120}$

$r=0.5$

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.