A geometric sequence is defined recursively by $a_{n} = 6 a_{n - 1}$ $a_n = 6a_(n -1)$ . The first term of the sequence is 0.75. Which of the following is the explicit formula for the nth term of the sequence?

Question

5020 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-12-23T07:25:30

$a_{n} = 0.75 \times {(6)}^{n - 1}$ $a_n = 0.75 xx (6)^(n-1)$

Given $a_{n} = 0.75$ $a_n = 0.75$

$a_{n} = 6 a_{n - 1}$ $a_n = 6a_(n - 1)$

$\Rightarrow \frac{a_{n}}{a_{n - 1}}$ $=> (a_n)/(a_(n-1)$ = 6

=> $r = 6$ $r = 6$

$a_{n} = a_{1} \times {(r)}^{n - 1}$ $a_n = a_1 xx (r)^(n-1)$

=> $a_{n} = 0.75 \times {(6)}^{n - 1}$ $a_n = 0.75 xx (6)^(n-1)$

A geometric sequence is defined recursively by a_n = 6a_(n -1)an=6an−1a_n = 6a_(n -1). The first term of the sequence is 0.75. Which of the following is the explicit formula for the nth term of the sequence?