What's the sum of the first five terms a1=8, r=3?

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Answer 1 · 2018-04-20T13:19:18

#968#.

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It is a geometric progression

We know that each term of a geometric progresion is constructed multipliying the prior term by a constant factor,

Thus in our case
#a_1=8#
#a_2=8·3=24#
#a_3=24·3=72#
#a_4=72·3=216# and finally
#a_5=216·3=648#

We have to sum #a_1+...+a_8#

You can do it using "manual" process or appliying sum formula for a geometric progresion

#8+24+72+216+648=968#

#S_n=(a_1(r^n-1))/(r-1)# for #n=5#. That is:

#S_5=(8(3^5-1))/(3-1)=1936/2=968#