Question

PLEASE HELP ME WITH MATH Write an explicit formula for the following sequence. Then generate the first five terms.

a = 625, r=0.2
Choose the correct explicit formula for the sequence.
O A. 2. = 0.2.(625)n-1 n> 1
O B. 2. = 625. (0.2)" – 1 for n21
O C. an = 625n-1 • (0.2) for n 21
OD. 2. = 625. (0-2)" for n> 1
Generate the first five terms.
24 = (Simplify your answer.)
az - (Simplify your answer.)
a3 = (Simplify your answer.)
Click to select your answer(s).

Answer 1

`\text{B. }a_n=625(0.2)^(n-1)\quad\text{for $n>1$}\\625,125,25,5,1`

Explanation:

The explicit formula for a geometric sequence with first term a1 and common ratio r is ...

`a_n=a_1\cdot r^(n-1)`

In this problem, you are given a1=625 and r=0.2. Filling in those values gives the explicit formula ...

`a_n=625(0.2)^(n-1)`

You can either evaluate this function for values of n = 1 through 5, or you can multiply each term by the common ratio to get the next.

a1 = 625

a2 = 625·0.2 = 125

a3 = 125·0.2 = 25

a4 = 25·0.2 = 5

a5 = 5·0.2 = 1