How do you write the first five terms of the geometric sequence $a_{n} = 5 a_{n - 1}$ $a_n = 5a_(n-1)$ ; $a_{1} = 3$ $a_1 = 3$ ?

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Answer 1 · 2016-01-19T13:55:38

$3, 15, 75, 375, 1875$ $3, 15, 75, 375, 1875$

$a_{n} = a_{1} r^{n - 1}$ $a_n = a_1r^(n - 1)$

$a_{n} = 5 a_{n - 1}$ $a_n = 5a_(n - 1)$

$a_{1} = 3$ $a_1 = 3$

$a_{2} = 3 r$ $a_2 = 3r$

But
$a_{2} = 5 a_{2 - 1} = 5 a_{1}$ $a_2 = 5a_(2 - 1) = 5a_1$

$\Rightarrow 3 r = 5 a_{1}$ $=> 3r = 5a_1$
$\Rightarrow 3 r = 5 \cdot 3$ $=> 3r = 5*3$
$\Rightarrow r = 5$ $=> r = 5$

Using $a_{n} = a_{1} r^{n - 1}$ $a_n = a_1r^(n - 1)$ with $a_{1} = 3$ $a_1 = 3$ and $r = 5$ $r = 5$ , the first 5 terms are

$3, 15, 75, 375, 1875$ $3, 15, 75, 375, 1875$

How do you write the first five terms of the geometric sequence a_n = 5a_(n-1)an=5an−1a_n = 5a_(n-1); a_1 = 3a1=3a_1 = 3?