This sequence is geometric, what is the next term 500, 250, 125, 62.5,...?

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Answer 1 · 2016-03-11T13:52:07

The next term in the series (5th term) : #=31.25#

#500, 250, 125, 62.5#

When provided with a geometric sequence we must first calculate the common ratio #r:#

#r# is obtained by dividing a term by its preceding term:

1) #250/500 =1/2#

2) #125/250 = 1/2#
For the sequence the common ratio # r = 1/2#.

Method 1:
the first term # a = 500#, and #n = 5# (We require the 5th term)

The 5th term can be obtained through formula:

# T_n = ar^(n-1) = 500 xx (1/2)^((5-1))#
#= 500 xx (1/2)^4#

#= 500 xx 1/16 = 500/16#

#T_5=31.25#

Method 2
We can find the fifth term by multiplying the 4th term by #r#

#T_5= T_4 xx 1/2#

# = 62.5 xx 1/2#

# = 62.5 /2#

# = 31.25#