If the third term of a geometric sequence is 36 and the eighth term is 8748, how do you find the first term?

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Answer 1 · 2015-11-08T08:53:25

#A_1 = 4#

#A_n = A_1r^(n - 1)#

#=> A_3 = A_1r^2#

#=> 36 = A_1r^2#

#A_8 = A_1r^7#

#=> 8748 = A_1r^7#

If we divide the second equation by the second

#8748/36 = (A_1r^7)/(A_1r^2)#

#=> 243 = r^5#

#=> r = 3#

Let's use the first equation to find #A_1#

#A_3 = A_1r^2#

#=> 36 = A_1*3^2#

#=> 36 = 9A_1#

#=> A_1 = 4#