Question

What is the sum of the geometric series in which a1 = 2, r = 3, and an = 486?

Sn = −1,254
Sn = −728
Sn = 81
Sn = 728

Answer 1

only by guessing a1=2,r=3,an=486
all are positive so sn can't be negative
first two options are deleted.
a1=2,an=486
so sum should be >486
so sn=728
but it is only a guess.
now we will proceed systematically.
\[an=a1 r^{n-1},486=2*3^{n-1},3^{n-1}=\frac{ 486 }{ 2 }=243=3^5\]
n-1=5
n=5+1=6
\[Sn=a1\frac{ r^{n} -1}{ r-1 }=2\frac{ 3^6-1 }{ 3-1 }=2\frac{ 729-1 }{ 2 }=728\]

Answer 2

That's the answer that I got! Thanks! I have a few more, do you think you will be able to help me?

Answer 3

@surjithayer

Answer 4

yes ,i will try.