Find the first six terms of the sequence.

a1 = 7, an = an-1 + 6

choices:
a. 13, 19, 25, 31, 37, 43

b. 0, 6, 12, 18, 24, 30

c. 7, 6, 12, 18, 24, 30

d. 7, 13, 19, 25, 31, 37

The correct answer to this question is this one: "D. 7, 13, 19, 25, 31, 37."

You can find a1+1 because you know the value of a1.

Now when you get to know the value of a1+1, you can get the value of a1+1+1. Repeat the cycle.

Because a2=a1+6, a2=7+6.
From that sequence, we can say that
a1 = 7
a2 = 13
a3 = 19
a4 = 25
a5 = 31
a6 = 37

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