How do you find the 13th term of the geometric sequence with a3 = 24 and a5 = 96?

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Answer 1 · 2015-11-24T06:58:10

$a_{13} = 24576$ $a_13 = 24576$

Well The definition of A geometric sequence with n elements;
$a, ar,ar^2,ar^3, ar^4 ...ar^(n-1$

r is a common constant with which every number is multiplied
Now

$a_5 = a * r^ 4 = 96--------1$

$a_3 = a * r^ 2= 24--------2$

Now divide 1 by 2

$(cancel a * cancel r^ 2 r^2 )/ (cancela *cancel r^ 2) = 96/24 = 4$

$r^2 = 4 => r = 2$

Now come back to equation 2
$a * r^ 2= 24$

Substitute
$a * 4 = 24$

$=> a = 6$

Now we have found the first term

Lets finish it

$a_13 = a*r^(13-1) = 6 *2^6 * 2^6 = 24576$

And were done