Answered

Westonci.ca is your trusted source for finding answers to a wide range of questions, backed by a knowledgeable community. Experience the convenience of getting reliable answers to your questions from a vast network of knowledgeable experts. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.

What is the third term in the geometric sequence [tex]\( f(n)=2(0.8)^{n-1} \)[/tex]?

A. 4.8
B. 2.56
C. 1.28
D. 1.024

Sagot :

GinnyAnswer
To find the third term in the geometric sequence [tex]\( f(n) = 2 \cdot (0.8)^{n-1} \)[/tex], follow these steps:

1. Identify the general form of the geometric sequence:
[tex]\[ f(n) = a \cdot r^{n-1} \][/tex]
where [tex]\( a \)[/tex] is the first term, [tex]\( r \)[/tex] is the common ratio, and [tex]\( n \)[/tex] is the term number.

2. Given the sequence, [tex]\( a = 2 \)[/tex] and [tex]\( r = 0.8 \)[/tex].

3. We are asked to find the third term ([tex]\( n = 3 \)[/tex]). Substitute [tex]\( n = 3 \)[/tex] into the general form of the sequence:
[tex]\[ f(3) = 2 \cdot (0.8)^{3-1} \][/tex]

4. Simplify the exponent [tex]\( 3-1 \)[/tex]:
[tex]\[ f(3) = 2 \cdot (0.8)^2 \][/tex]

5. Calculate [tex]\( (0.8)^2 \)[/tex]:
[tex]\[ (0.8)^2 = 0.64 \][/tex]

6. Multiply [tex]\( 2 \)[/tex] by [tex]\( 0.64 \)[/tex]:
[tex]\[ f(3) = 2 \cdot 0.64 = 1.28 \][/tex]

The third term in the geometric sequence [tex]\( f(n) = 2 \cdot (0.8)^{n-1} \)[/tex] is [tex]\( 1.28 \)[/tex].

Therefore, the answer is [tex]\(\boxed{1.28}\)[/tex].
Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.