Question

Create an explicit formula of the sequence. 7, 14, 28, 56, .... Find the 10th term of the sequence. Complete your work in
the space provided.or upload a file that can display math symbols if your work requires it. In your answer, be sure to
include the explicit formula and the 10th term of the sequence.

Answer 1

Answer:

3584

Step-by-step explanation:

These are the terms of a geometric sequence with n th term

$a_{n}$ = a$(r)^{n-1}$

where a is the first term and r the common ratio

r = 14 ÷ 7 = 28 ÷ 14 = 56 ÷ 28 = 2 and a = 7, thus

$a_{10}$ = 7$(2)^{9}$ = 7 × 512 = 3584

Answer 2

The 10th term of the given geometric sequence is 3584.

What is a geometric sequence?

"Geometric sequence, is a sequence of non-zero numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio."

Given sequence is: 7, 14, 28, 56,......

The first term of the sequence(a)  is 7.

Therefore, $7 = (7)(1) = (7)(2)^{0} = a(r)^{1-1}$

The second term of the sequence is 14.

Therefore, $14 = (7)(2) = (7)(2)^{1} = a(r)^{2-1}$

Here, r = common ratio = 2

Similarly, the third term of the sequence is 28.

Therefore, $28 = (7)(4) = (7)(2)^{2} = a(r)^{3-1}$

Similarly, the 4th term of the sequence is 56.

Therefore, $56 = (7)(8) = (7)(2)^{3} = a(r)^{4-1}$

Therefore, the given sequence is a geometric sequence where the first term is '7' and the common ratio is '2'.

The 10th term (n=10) of the sequence is

$= a.r(10-1)= ar^{9} = (7)(2)^{9}= (7)(512) = 3584$

Learn more about a geometric sequence here: https://brainly.com/question/11266123

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