Question

Find the geometric sum: 6 + 12 + 24 + … + 6,144

Answer 1

`a_1=6\\r=2\\a_n=6144\\S_n=(a_1(1-r^n))/(1-r)\\\\a_n=a_1r^(n-1)\\6144=6\cdot 2^(n-1)\\2^(n-1)=1024\\2^(n-1)=2^(10)\\n-1=10\\n=11\\\\S_(11)=(6(1-2^(11)))/(1-2)=(6\cdot(-2047))/(-1)=12282`

Answer 2

Explanation:

The answer of this geometric sum is:

6+12+24+48+96+192+384+768+1,536+3,072+6,144.

=12,282

When you are finding the geometric sum of something, you just add the each term in the sequence. Like,

6+6=12

12+12=24

24+24=48

48+48= 96

and so on..

Thus the sum is 12,282....