The geometric sequence 20, 60, 180, 540,.........., 393 660 has how many terms?

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Answer 1 · 2015-11-08T10:00:59

$n = 10$ $n = 10$

$A_{n} = A_{1} r^{n - 1}$ $A_n = A_1r^(n - 1)$

$A_{1} = 20$ $A_1 = 20$

$A_{2} = 60 = A_{1} r^{2 - 1}$ $A_2 = 60 = A_1r^(2-1)$

$\Rightarrow 60 = 20 r$ $=> 60 = 20r$
$\Rightarrow r = 3$ $=> r = 3$

$A_{n} = 393660 = A_{1} r^{n - 1}$ $A_n = 393660 = A_1r^(n - 1)$

$\Rightarrow 393660 = 20 \cdot 3^{n - 1}$ $=> 393660 = 20*3^(n -1)$

$\Rightarrow 19683 = 3^{n - 1}$ $=> 19683 = 3^(n-1)$

$\Rightarrow 3^{9} = 3^{n - 1}$ $=> 3^9 = 3^(n - 1)$
$\Rightarrow 9 = n - 1$ $=> 9 = n - 1$

$\Rightarrow n = 10$ $=> n = 10$