What is a formula for the nth term of the given sequence? 48, 72, 108

Mathematics

1 answer:

WITCHER [35]3 years ago

7 0

Answer:

$a_n=48*1.5^{n-1}$

Step-by-step explanation:

Geometric Sequence

In geometric sequences, each term is found by multiplying (or dividing) the previous term by a fixed number, called the common ratio.

We are given the sequence:

48, 72, 108, ...

The common ratio is found by dividing the second term by the first term:

$r=\frac{72}{48}=1.5$

To ensure this is a geometric sequence, we use the ratio just calculated to find the third term a3=72*1.5=108.

Now we are sure this is a geometric sequence, we use the general term formula:

$a_n=a_1*r^{n-1}$

Where a1=48 and r=1.5

$\boxed{a_n=48*1.5^{n-1}}$

For example, to find the 5th term:

$a_5=48*1.5^{5-1}=48*1.5^{4}=243$

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3 years ago

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100 points (algebra one) describe and correct the error in comparing the graphs

Pepsi [2]

Answer:

The error made is that the graph of $y=x^{2} +3$ is a vertical translation up by 3, instead of down.

Step-by-step explanation:

Exponential functions, when they are graphed, use the function $f(x)=a(x-h)^{2} +k$ .

In the equation, k expresses how much the graph shifts vertically. In this case, the function shifts vertically up by 3 from the parent function, $y=x^{2}$ . So, the translation is actually 3 units up compared to the graph of $y=x^{2}$ .