Question

Find the sum of the following series. Round to the nearest hundredth if necessary 6 + 12 + 24 + ... + 6144

Answer 1

Solution

for this case we can write the following general expression:

$a_n=a_1(r)^{n-1}$

And for this case a1= 6

We can find the value of r like this:

$12=6(r)^{2-1}$

r= 2

and then the equation would be given by:

$a_n=6(2)^{n-1}$

then the sum would be:

6+12+24+48+ 96+ 192+384+768+1536+3072+6144=12282