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:
[tex]r=\dfrac{a_2}{a_1}[/tex]
[tex]r=\dfrac{560}{1120}[/tex]
[tex]r=0.5[/tex]
The nth term of a geometric sequence is:
[tex]a_n=ar^{n-1}[/tex]
Where a is the first term and r is the common ratio.
Putting [tex]a=1120, r=0.5[/tex], we get
[tex]a_n=1120(0.5)^{n-1}[/tex]
Therefore, the required formula for the given sequence is [tex]a_n=1120(0.5)^{n-1}[/tex].
We need to find the 10th term of the given sequence. So, substituting [tex]n=10[/tex] in the above formula.
[tex]a_{10}=1120(0.5)^{10-1}[/tex]
[tex]a_{10}=1120(0.5)^{9}[/tex]
[tex]a_{10}=1120(0.001953125)[/tex]
[tex]a_{10}=2.1875[/tex]
Therefore, the 10th term of the given sequence is 2.1875.
