Answer:
10th term of the sequence = 0.537
Step-by-step explanation:
First three terms of the sequence are → 5, 4, [tex]\frac{16}{5}[/tex]..........
Ratio of 2nd and 1st term of the sequence = [tex]\frac{4}{5}[/tex]
Ratio of 3rd and 2nd term of the sequence = [tex]\frac{\frac{16}{5} }{4}[/tex]
= [tex]\frac{4}{5}[/tex]
Therefore, ratio between every successive term to the previous term is common.
Common ratio 'r' = [tex]\frac{4}{5}[/tex]
First term of the sequence 'a' = 5
nth term of a geometric sequence = [tex]a(r)^n[/tex]
Therefore, nth term of the given term will be [tex]T_n=5(\frac{4}{5})^n[/tex]
Now we have to find the 10 term of the given sequence.
For n = 10,
[tex]T_{10}=5(\frac{4}{5})^{10}[/tex]
= 0.53687
≈ 0.537
Therefore, 10th term of the sequence is 0.537
