If the fifth and sixth terms of a geometric sequence are 8 and 16, respectively, then what is the first term?

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Answer 1 · 2016-12-03T14:30:41

Since these are consecutive terms, we can use the formula #r = t_n/t_(n - 1)#, where #r# is the common ratio of the sequence.

#r = t_n/t_(n - 1)#

#r= 16/8#

#r = 2#

We now can solve for #a# in the formula for the nth term of a geometric sequence, #t_n = a xx r^(n - 1)#, if we plug in one of the terms.

Let's use #t_6 = 16#.

#16 = a xx 2^(6 - 1)#

#16 = a xx 2^5#

#16 = 32a#

#a = 16/32#

#a = 1/2#

#:.#The first term is #1/2#.

Hopefully this helps!