Wednesday

May 4, 2016
Posted by **kareema** on Friday, January 3, 2014 at 11:22am.

- math -
**Steve**, Friday, January 3, 2014 at 12:14pm2+4+8+...+2^n = 2^(n+1)-2

- math -
**Chelle**, Friday, January 3, 2014 at 1:32pm2,4,8,16,......

This is a geometric sequence. That means the same number is multiplied, which is 2.

You could calculate this way;

{a, ar, ar^2, ar^3, ar^4, …..}

2, 2x2 2x2^2 2x2^3 2x2^4

(2, 4, 8, 16, 32, ...)

a = the 1st term.

common ratio = 2 > the factor between terms.

Formula:

an = ar^(n - 1)

an = 2 x 2^(n – 1)

a = 2 > 1st term

r = 2 > common ratio

n = nth term > the term you're going to.

The third and fourth term you already know.

a(3)= 2 x 2^(3 - 1)

a(3)= 2 x 2^2

a(3)= 2 x 4

a(3) = $8

a(4)= 2 x 2^(4 - 1)

a(4)= 2 x 2^3

a(4)= 2 x 8

a(4)= $16

a(12)= 2 x 2^(12 - 1)

a(12)= 2 x 2^11

a(12)= 2 x 2048

a(12)= %4096

Answer:

$4096 - math -
**Steve**, Friday, January 3, 2014 at 5:40pmChelle's solution gives the 12th term, but does not show the sum of all 12 terms, which was what was asked.