A recursive rule for a geometric sequence is a1 = 9; an = 2/3 (an−1)

What is the iterative rule for this sequence?

A.) an = 9 • (2/3)^n
B.) an = 2/3 • 9^n
C.) an = 9 • (2/3)^n-1

C.

Step-by-step explanation:

Iterative geometric sequence:

Recursive geometric sequence:

The equations are very similar and you only really need to rearrange it. The factor (2/3) and the first term (9) are given, so you can write the iterative equation:

And so the answer is C.

The relationship between <7 and <8 can be said to be vertically opposite angles. They are equal to one another and formed by the intersection of two straight lines. i.e. the intersection of lines C and D.

The special angles created by the intersection of lines C and D can be used to solve for y because they all are inter woven and connected to one another either supplemtarily or by being vertically opposite angles.

5y - 29 = 3y + 19( vertically opposite angles)

5y - 3y = 19 + 29

2y = 48

y = 48/2

= 24.

<7 = <8

<7 + 5y - 29 = 180°( angles on a straight line)

<7 = 180° + 29 - (5 × 24)

= 209 - 120

<7 = 89°

<8 = 89° (vertically opposite angles)