Question

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

Answer 1

Answer:

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

Step-by-step 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