6.(08.04)
what is the sum of the geometric sequence 2, 8, 32, if there are 8 terms?

43,690.

Step-by-step explanation:

The common ratio r is 8/2 = 32/8 = 4.

Sum of n terms = a1 * (r^n - 1) / (r - 1).

a1 = 2 and r = 4 so

Sum of 8 terms = 2 *(4^8 - 1) / (4 - 1)

= 2 * 65535 / 3

= 43,690.

x = central angle apc = measure of minor arc ac

the two angles x and 30 add to 180, so x+30 = 180 and x = 180-30 = 150. the measure of minor arc ac is 150 degrees.

what we need to do from here is find the circumference and then multiply it by x/360 since there are 360 degrees in a circle. in this case, x = 150, so x/360 = 150/360 = 15/36 = 5/12. the shortest distance along the curve from a to c is 5/12 of the distance around the entire circle (aka circumference)

c = circumference

c = pi*d

c = pi*24

c = 24pi

now multiply this by 5/12 to get

distance along minor arc ac = (5/12)*(circumference)

distance along minor arc ac = (5/12)*(24pi)

distance along minor arc ac = 10pi

the formula you can use is

l = (x/360)*pi*d

with

l = length of minor arc

x = central angle

d = diameter

which essentially is the steps we took though a bit differently.

true

explanation: