A geometric sequence is defined by the explicit formula $a_{n} = 3 {(- 5)}^{n - 1}$ $a_n = 3(-5)^(n-1)$ , what is the recursive formula for the nth term of this sequence?

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Answer 1 · 2017-01-05T21:07:17

$a_{1} = 3; a_{n + 1} = a_{n} (- 5)$ $a_1=3; a_(n+1)=a_n(-5)$

The first term ( $a_{1}$ $a_1$ ) is 3.

The second one ( $a_{2}$ $a_2$ ) is obtained by multiplyng $3 \cdot (- 5)$ $3*(-5)$

The third one ( $a_{3}$ $a_3$ ) by multiplying $3 \cdot (- 5) (- 5) = a_{2} \cdot (- 5)$ $3*(-5)(-5)=a_2*(-5)$

and so on.

Then

$a_{1} = 3; a_{n + 1} = a_{n} (- 5)$ $a_1=3; a_(n+1)=a_n(-5)$

A geometric sequence is defined by the explicit formula a_n = 3(-5)^(n-1)an=3(−5)n−1a_n = 3(-5)^(n-1), what is the recursive formula for the nth term of this sequence?