paulinaxu0430
Answered

At Westonci.ca, we connect you with experts who provide detailed answers to your most pressing questions. Start exploring now! Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.

The first term of a sequence is 5. Each term after the first is 3 times the preceding term. If [tex]$x$[/tex] represents the [tex]$m$[/tex]th term of the sequence, which equation gives [tex][tex]$x$[/tex][/tex] in terms of [tex]$m$[/tex]?

A. [tex]$x = 5\left(3^m\right)$[/tex]
B. [tex][tex]$x = 5\left(3^{m-1}\right)$[/tex][/tex]
C. [tex]$x = 3\left(5^m\right)$[/tex]
D. [tex]$x = 3\left(5^{3m-1}\right)$[/tex]

Sagot :

GinnyAnswer
Given the sequence with the first term as 5, and each subsequent term being 3 times the preceding term, we can establish that this sequence is geometric with the first term ([tex]\(a\)[/tex]) equal to 5 and the common ratio ([tex]\(r\)[/tex]) equal to 3.

For a geometric sequence, the [tex]\(n\)[/tex]-th term is given by:
[tex]\[ a_n = a \cdot r^{n-1} \][/tex]

Here, [tex]\(a = 5\)[/tex] and [tex]\(r = 3\)[/tex]. Therefore, the [tex]\(m\)[/tex]-th term of the sequence, [tex]\(x\)[/tex], can be written as:
[tex]\[ x = 5 \cdot 3^{m-1} \][/tex]

Thus, the correct equation for [tex]\(x\)[/tex] in terms of [tex]\(m\)[/tex] is:

(B) [tex]\(\boxed{x = 5 \cdot 3^{m-1}}\)[/tex]
Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. We appreciate your time. Please come back anytime for the latest information and answers to your questions. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.