The 8th term of the sequence is 4374.
Step-by-step explanation:
It is given that,
- The first term of a geometric sequence is 2, and the common ratio is 3.
- You need to find the 8th term of the sequence.
The general form of geometric sequence is a, ar, ar²,ar³,.......
where,
-
a is the first term of the sequence. Here, the first term a = 2
- r is the common ratio. Here, the common ratio r = 3.
The formula to find the nth term of the geometric sequence is given by :
⇒ [tex]n_{th} term = ar^{n-1}[/tex]
The question is asked to find the 8th term. Hence n = 8.
⇒ [tex]8_{th} term = 2 \times 3^{8-1}[/tex]
⇒ [tex]2 \times 3^{7}[/tex]
⇒ [tex]2 \times 2187[/tex]
⇒ [tex]4374[/tex]
∴ The 8th term of the sequence is 4374.
