Question

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

Answer 1

10th term of the sequence = 0.537

Explanation:

First three terms of the sequence are → 5, 4,
`(16)/(5)`..........

Ratio of 2nd and 1st term of the sequence =
`(4)/(5)`

Ratio of 3rd and 2nd term of the sequence =
`((16)/(5) )/(4)`

=
`(4)/(5)`

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

Common ratio 'r' =
`(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((4)/(5))^n`

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

For n = 10,

`T_(10)=5((4)/(5))^(10)`

= 0.53687

≈ 0.537

Therefore, 10th term of the sequence is 0.537