What is the term-to-term rule to this sequence? 64, 32, 16, 8, 4

1 Answer
LM
Jun 8, 2018

#a_n = 1/2a_(n-1)#

Explanation:

#64, 32, 16, 8, 4#
is a geometric sequence.

this is a sequence where, to get from one term to the next, there is a number that you have to multiply it by. this is the same for all parts of the sequence.

#64/2 = 32#
#32/2 = 16#
etc.

to get from #64# to #32#, you divide by #2#.
this is the same as multiplying by #1/2#

#64 * 1/2 = 64/1 * 1/2 = 64/2 = 32#

hence, the number that each term is multiplied by to find the next is #1/2#.

if we call one term #a_n# and the previous term #a_(n-1)#, where #n# shows position in the sequence and therefore that #a_n# is one ahead of #a_(n-1)#, then we find that #a_n = 1/2a_(n-1)#.

this is the notation for the term-to-term rule, using #n# for the current position, #n-1# for the position before, and #a_n# with #a_(n-1)# to show progress from one position to the next.

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