The common ratio of an infinite geometric series is 11/16, and its sum is 76 4/5, how do you find the first four terms of the series?
1 Answer
Aug 23, 2017
The first four terms of the series are:
#24, 33/2, 363/32, 3993/512#
Explanation:
The general term of a geometric series is given by the formula:
#a_n = ar^(n-1)#
where
The sum of the first
#s_N = (a(1-r^N))/(1-r)#
If
#s_oo = lim_(N->oo) s_N = a/(1-r)#
In our example, we are told:
#{ (r = 11/16), (s_oo = 76 4/5 = 384/5) :}#
Hence:
#384/5 = s_oo = a/(1-r) = a/(1-11/16) = (16a)/5#
Multiplying both ends by
#a = 24#
So the first four terms are:
#24#
#24*11/16 = 33/2#
#33/2*11/16 = 363/32#
#363/32*11/16 = 3993/512#