What are the first three terms of a geometric sequence with a common ratio of #2/5# if the sixth term is #64/25#?

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Answer 1 · 2016-07-26T01:40:39

#a_1 =250, a_2 = 100, a_3 =40#

The #n^(th)# term of a geometric sequence is given by:

#a_n = a_1r^(n-1)# Where #r# is the Common Ratio and #a_1# is the #1^(st)# term.

In this example; #r=2/5, n=6 #
Thus, #a_6 =a_1r^(6-1)#

We are told that #a_6 = 64/25 -> 64/25 = a_1 * (2/5)^5#

Hence, #a_1 = 64/25 * 5^5/2^5 = 2^6/5^2 * 5^5/2^5#

#a_1=2^1* 5^3 = 2 * 125 = 250#

#a_2 = 250 * 2/5 = 100#
#a_3 = 100 *2/5 = 40#