Question

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

Answer 1

Answer:

Step-by-step 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....

Answer 2

$a_1=6\\r=2\\a_n=6144\\S_n=\dfrac{a_1(1-r^n)}{1-r}\\\\a_n=a_1r^{n-1}\\6144=6\cdot 2^{n-1}\\2^{n-1}=1024\\2^{n-1}=2^{10}\\n-1=10\\n=11\\\\S_{11}=\dfrac{6(1-2^{11})}{1-2}=\dfrac{6\cdot(-2047)}{-1}=12282$