Answer:
[tex]a_5 = 32[/tex]
Step-by-step explanation:
The nth term for the geometric sequence is given by:
[tex]a_n = a_1 \cdot r^{n-1}[/tex]
where,
[tex]a_1[/tex] is the first term
r is the common ratio
n is the number of terms.
As per the statement:
For the geometric sequence of [tex]a_1=2[/tex] and r=2
We have to find [tex]a_5[/tex]
for n = 5;
[tex]a_5=a_1 \cdot r^{n-1}[/tex]
Substitute the given values we have;
[tex]a_5 = 2 \cdot 2^4 = 2 \cdot 16[/tex]
⇒[tex]a_5 = 32[/tex]
Therefore, the value of [tex]a_5[/tex] is, 32
