Find the missing terms of the geometric sequence 480,12.288, …. (hint: the geometric mean of the first and fifth terms is the third term.)

To solve this problem  you must apply the proccedure shown below:
 1. You have:
 480r^(5-1)=12.288
 480r^4=12.288
 r^4=12.288/480
 r=(12.288/480)^(1/4)
 r=0.4
 2. Now, multiply r=0.4 to each term, as below:
 480x0.4=192
 192x0.4=76.8
 76.8x0.4=30.72
 30.72x0.4=12.288
 Therefore, as you can see, the answer is: 192,76.8,30.72

Intersecting secant-tangent theorem states that if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.so to break it down: 1. pq acts as the tangent and ps as the secant with an intersection at p.sr = 21rp = 3x + 3pq = 4x + 4following to equation: tangent squared = the two segments multiplied by each otherso (4x + 4) ^ 2 = (3x + 3) • (21) simplifies to 16x^2 - 31x - 47 = 0 or (16x - 47)(x + 1) x = -1 or x = 47/162. pq acts as the tangent and ps as the secant with an intersection at p (again! )sr = 16rp = xpq = 15(15) ^ 2 = 16 • x225 = 16xx = 225/163. the interesting chords are proportional to each other so a ratio is possible to set up: ap dp 10 3 + x = = —— = pc pb 8 xcross multiple to get 10x = (3 + x)(8)x = 12