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

Answer:

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

Step-by-step 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.