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 #

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