Question

Can't figure out this problem can anyone help if so thank you

Answer 1

Answer:

10th term of the sequence = 0.537

Step-by-step explanation:

First three terms of the sequence are → 5, 4, $\frac{16}{5}$..........

Ratio of 2nd and 1st term of the sequence = $\frac{4}{5}$

Ratio of 3rd and 2nd term of the sequence = $\frac{\frac{16}{5} }{4}$

                                                                        = $\frac{4}{5}$

Therefore, ratio between every successive term to the previous term is common.

Common ratio 'r' = $\frac{4}{5}$

First term of the sequence 'a' = 5

nth term of a geometric sequence = $a(r)^n$

Therefore, nth term of the given term will be  $T_n=5(\frac{4}{5})^n$

Now we have to find the 10 term of the given sequence.

For n = 10,

$T_{10}=5(\frac{4}{5})^{10}$

      = 0.53687

      ≈ 0.537

Therefore, 10th term of the sequence is 0.537