How do you write an explicit formula for the sequence ? 640,160,40,10,..

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Answer 1 · 2018-02-26T01:42:59

#a_n=640*(1/4)^(n-1)#

This is a geometric sequence; the ratio of two consecutive terms is the same:

#160/640=1/4#

#40/160=1/4#

#10/40=1/4#

The explicit or general formula of a geometric sequence is

#a_n=a_1*r^(n-1)# with #a_1# as the first term, #r# as the common ratio, and #n# as the #n^(th)# term.

Plug in:

#a_n=640*(1/4)^(n-1)#

Double Check:

#a_2=640*(1/4)^(2-1)=640/4=160#