The next term of the sequence is 64 since the given sequence is a geometric sequence. So, the given statement is false i.e., the next term is 48.
What is a geometric sequence?
A sequence in which the ratio of two consecutive terms is the same. I.e., the sequence has the common ratio (ratio of a term to the previous term).
The nth term of the sequence is calculated as follows:
[tex]a_n = a_1*r^(^n^-^1^)[/tex]
Where,
a_n - nth term
a1 = first term
r = common ratio
n - the number of the required term in the sequence.
Calculating the next term in the given sequence?
The given sequence is {2, 4, 8, 16, 32, ...}
So, the required term is at the 6th position in the sequence. I.e., n = 6
First term a1 = 2, common ratio r = 4/2 = 8/4 = 16/8 = 2
Then, the 6th term in the sequence is
[tex]a_6 = (2)*(2)^(^6^-^1^)[/tex]
= 2 × [tex]2^5[/tex]
= 2 × 32
= 64
So, the next term in the given sequence is 64 but not 48. So, the given statement is false.
Learn more about the geometric sequence here:
https://brainly.com/question/24643676
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