Find the next three terms.

-1, 2, -4, 8, -16

This is a geometric sequence, that is, a sequence where each successive integer is a result of multiplying the previous one by a fixed, non-zero number called the common ratio.  We need to find which number is the common ratio and then complete the next three terms using that ratio.  If we look at the first and second numbers, we need to ask "what can we multiply by -1 to get 2".  If it's not obvious to you, try looking at the next two numbers... what can you multiply by 2 to get -4.  The answer is -2.

 -1 x -2 = 2
2 x -2 = -4
-4 x -2 = 8
etc...

So we need to go to the end of the sequence and find the next three numbers...

-16 x -2 = 32
32 x -2 = -64
-64 x -2 = 128

Next three numbers in the sequence are 32, -64, 128

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