Question

PLEASE!!!! I know I have the formula done correctly but I'm not coming up with the right answer:
what is the sum of the geometric series. Sigma 6(2)^x where n=1 and 10 in the series.
I have 6(2)^x +6(2)^x....10 times. Answer choices are a:15,658 b: 6,138 c:12,276 d: 756
I keep coming up with 1,440

Answer 1

\[\sum_{n=1}^{10}6(2)^x\]

Answer 2

I think this is written confusingly. Normally it would be x=1 > x=10. i.e the symbol under the sigma sign should read x=1.
(alternatively it should be 2^n rather than 2^x).

If that is the case then it means :
for each value of x from 1 to 10 add up the value of 6(2)^x

Note that as the 6 is constant you can remove it from the Summation and 'multiply'

so it becomes 6* sum(2^1,2^2...........2^10)

You might notice that summing the powers of 2 is like a binary number so you have
11111111110 in binary (the 0 is because there is no 2^0 term) convert and multiply by 6....

Answer 3

I agree it is written strangely. And that they should all be either "x" or "n". But you lost me with the explanation. I really have no idea how to get to one of the answers listed.

Answer 4

so it would be: 6(2)+6(4)+6(8)....out 10 terms?

Answer 5

Yes that is correct - and it does come to one of the answers.

My binary explanation may be a little off the topic - but it does give a quick way to come to the answer. But your way will work too..

Answer 6

That does work out to one of the answers

Answer 7

Thank you so much!

Answer 8

Here a=2, r=2>1,n=10
∑_(x=1)^10▒〖6(2)^x=6{∑_(x=1)^10▒2^x } 〗=6{2^1+2^2+2^3…+2^10 }
Sn=a(r^n-1)/(r-1),n>1
S10=2(2^10-1)/(2-1)=2(2^10-1)
Total solution=6*2(2^10-1)=12(1024-1)=12*1023=?