Middle School

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Write an explicit formula for the following sequence. Then generate the first five terms.

Given: \( a = 625, r = 0.2 \)

Choose the correct explicit formula for the sequence.

A. \( a_n = 625 \cdot (0.2)^{n-1} \) for \( n \geq 1 \)
B. \( a_n = 625 \cdot (0.2)^{n-1} \) for \( n \geq 1 \)
C. \( a_n = 625 \cdot (0.2) \cdot (n-1) \) for \( n \geq 1 \)
D. \( a_n = 625 \cdot (0.2)^n \) for \( n \geq 1 \)

Generate the first five terms.

\[ a_1 = \] (Simplify your answer.)

\[ a_2 = \] (Simplify your answer.)

\[ a_3 = \] (Simplify your answer.)

\[ a_4 = \] (Simplify your answer.)

\[ a_5 = \] (Simplify your answer.)

Click to select your answer(s).

Answer :

Answer:

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

Step-by-step explanation:

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

[tex]a_n=a_1\cdot r^{n-1}[/tex]

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

[tex]a_n=625(0.2)^{n-1}[/tex]

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

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Rewritten by : Jeany

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