Question

If $2000 is invested at 5% interest, compounded annually, then after n years the investment is worth an = 2000(1.05)n dollars. (a) Find the first five terms of the sequence {an}. (Round your answers to the nearest cent.)

Answer 1

The first five terms of the sequence are: 2000, 2100, 2205, 2315.25, 2431.01.

Explanation:

The sequence is modeled by the equation:

`a_(n) = 2000(1.05)^(n)`

(a) Find the first five terms of the sequence {an}.

`a_(n) = 2000(1.05)^(n)`

`a_(0) = 2000(1.05)^(0) = 2000`

`a_(1) = 2000(1.05)^(1) = 2100`

`a_(2) = 2000(1.05)^(2) = 2205`

`a_(3) = 2000(1.05)^(3) = 2315.25`

`a_(4) = 2000(1.05)^(4) = 2431.01`

The first five terms of the sequence are: 2000, 2100, 2205, 2315.25, 2431.01.