Question

The next term of the sequence is 48.
(2, 4, 8, 16, 32,...)

Answer 1

Answer:

64

Step-by-step explanation:

Note that each new term of this geometric sequence is 2x the previous term.

If the sequence starts off as 2, 4, 8, 16, 32 ... , then the next term is 2(32) = 64.

(Where did the '48' come from?)

Answer 2

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:

$a_n = a_1*r^(^n^-^1^)$

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

$a_6 = (2)*(2)^(^6^-^1^)$

    = 2 × $2^5$

    = 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

#SPJ2