Question

Determine the explicit form of the function that describes the sequence below. 16, 24, 36, 54

Answer 1

Answer:

$a_n=16*(\frac{3}{2})^{(n-1)}$

Step-by-step explanation:  

We have been given a sequence and we are asked to write an explicit formula for our given sequence.

16, 24, 36, 54

We can see from our given sequence that difference between two consecutive terms is not same, therefore our given sequence is a geometric sequence.

A geometric sequence is in form: $a_n=a_1*r^{(n-1)}$, where

$a_n$= nth term of the sequence.

$a_1$= 1st term of sequence,

r = Common ratio between two consecutive terms.

We can see that 1st term of our given sequence is 16.

Let us find common ratio of our given sequence by dividing one number of our sequence by its preceding number in the sequence.  

$\text{Common ratio}=\frac{24}{16}$

$\text{Common ratio}=\frac{3}{2}$

Let us substitute our values in explicit formula to get our desired formula.

$a_n=16*(\frac{3}{2})^{(n-1)}$

Therefore, our desired explicit formula will be $a_n=16*(\frac{3}{2})^{(n-1)}$.