Which represents the sum of the geometric series: 6 + 12 + 24 + 48 + … + 12,288?
12,372

13,818

18,426

24,570

First, we need to solve for the common ratio from the data given by using the equation.

a(n) = a(1) r^(n-1)
12 = 6 r^(2-1)
r = 2

12288 = (6) 8^(n-1)

2048 = 8^(n-1)

 n = 11

Then, we can find the sum by:

Sum of terms inside the brackets is 4095, i.e. 2^12 - 1. 
So the required sum = 6 x 4095 
= 24,570

the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

                      )

triangle abd and cba are similar,

                            (2)

triangle cad and cba are similar,

                      )

using (1), (2) and (3), we get

hence proved.

therefore option 2 is correct.