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

Sagot :

elcharly64

Answer:

[tex]a_n=48*1.5^{n-1}[/tex]

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:

[tex]r=\frac{72}{48}=1.5[/tex]

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:

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

Where a1=48 and r=1.5

[tex]\boxed{a_n=48*1.5^{n-1}}[/tex]

For example, to find the 5th term:

[tex]a_5=48*1.5^{5-1}=48*1.5^{4}=243[/tex]

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