The first term of an infinite geometric series is -8, and its sum is -13 1/3, how do you find the first four terms of the series?

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Answer 1 · 2017-02-25T10:30:14

#-8, -16/5, -32/25, -64/125#

We need to find the common ratio first.

#" for the GP "a, ar,ar^2,....ar^(n-1)#

#a=-8, S_oo=-13 1/3=-40/3#

the formula for sum to infinity:#" "S_oo=a/(1-r), |r|<1#

in this case#" " -40/3=-8/(1-r)#

#cancel(-40)^5(1-r)=3xxcancel(-8)#

#5-5r=3#

#2=5r=>r=2/5#

#a=-8#

#ar=-8xx2/5=-16/5#

#ar^2=-16/5xx2/5=-32/25#

#ar^3=-32/25xx2/5=-64/125#

first four terms

#-8, -16/5, -32/25, -64/125#