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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]
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