Question

18
which of the following function represents this sequence? (a.fgr.9.4)

n	$a_n$
2	8
3	16
4	32
5	64
...	...

a $a_n = 4 \cdot 2^{n-1}$
b $a_n = 2^{n-1}$
c $a_n = 4^{n-1}$
d $a_n = 2 \cdot 4^{n-1}$

Explanation:

Step1: Identify sequence type

This is a geometric sequence where each term is multiplied by 2 to get the next term. The first term $a_1=4$, common ratio $r=2$.

Step2: Recall geometric sequence formula

The general formula for a geometric sequence is $a_n = a_1 \cdot r^{n-1}$.

Step3: Substitute values into formula

Substitute $a_1=4$ and $r=2$:
$a_n = 4 \cdot 2^{n-1}$

Step4: Verify with given terms

For $n=1$: $4 \cdot 2^{1-1}=4 \cdot 1=4$
For $n=2$: $4 \cdot 2^{2-1}=4 \cdot 2=8$
For $n=3$: $4 \cdot 2^{3-1}=4 \cdot 4=16$, which matches the table.

Answer:

A. $a_n = 4 \cdot 2^{n-1}$