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Which sequence is modeled by the graph below? coordinate plane showing the points 1, 4; 2, 0.8; and 3, 0.16

an = 4(−5)n − 1
an = 4(one fifth)n − 1
an = 0.4(5)n − 1
an = one fifth(4)n − 1

User Hrdwdmrbl
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2 Answers

4 votes
2nd one: an = 4(1/5)^n - 1
User Nate Potter
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8.4k points
4 votes

Answer:

Option 2nd is correct


a_n = 4 \cdot ((1)/(5))^(n-1)

Explanation:

The nth term for the geometric sequence is given by:


a_n = a_1 \cdot r^(n-1) ....[1]

where,


a_1 is the first term

r is the common ratio term

n is the number of terms.

As per the statement:

Given the coordinates points:

(1, 4), (2, 0.8) and (3, 0.16)

We can write this as:

n
a_n

1` 4

2 0.8

3 0.16

This is a geometric series

Here,
a_1 = 4 and common ratio(r) =
(1)/(5)

Since,


(0.8)/(4) = 0.2 = (1)/(5)


(0.16)/(0.8) = 0.2 = (1)/(5)

Substitute the given values in [1] we have;


a_n = 4 \cdot ((1)/(5))^(n-1)

Therefore, the sequence is modeled by the given graph is:


a_n = 4 \cdot ((1)/(5))^(n-1)

Which sequence is modeled by the graph below? coordinate plane showing the points-example-1
User Sudantha
by
9.0k points

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