the sum of the first 8 terms of a geometric sequence is 6560. The common ratio is 3. What is the third term of the sequence?

generals336 2020-11-09 Answered
the sum of the first 8 terms of a geometric sequence is 6560. The common ratio is 3. What is the third term of the sequence?
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hesgidiauE
Answered 2020-11-10 Author has 106 answers

The formula for the sum of nn terms of a geometric sequence is Sn=a1(1rn)(1r) where a1 is the first term and rr is the common ratio.
If the sum of the first n=8 terms is S8=6560 and the common ratio is r=3, then:
S8=a1(138)13
6560=a1(16561)2
6560=6560a12
6560=3280a1
2=a1
Now that we know a1, we can find the third term. The nnth term of a geometric sequence is given by the formula an=a1rn1.
Since a1=2,r=3, and n=3 for the third term, then:
a3=2(3)31=2(3)2=2(9)=18

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