How do you write a geometric series for which r=1/2 and n=4?

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Answer 1 · 2016-12-05T08:49:36

#a_1, a_1/2, a_1/4, a_1/8# Where #a_1# is the first term in the series

In general the #n^(th)# term of a geometric sequence is given by:

#a_n = a_"n-1"*r# Where #r# is the common ratio and #a_1# is the first term.

In this example, #r=1/2# and #n=4#

#a_2 = a_1* 1/2#

#a_3 = a_2*1/2 = a_1*1/4#

#a_4 = a_3*1/2 = a_1*1/8#

In general, #a_n = a_1/2^(n-1)#

Hence: the series requested is:

#a_1, a_1/2, a_1/4, a_1/8# Where #a_1# is the first term in the series