State the geometric sequence both recursive and explicit formulas.

recursive formula =

explicit formula:

Step-by-step explanation:

Thinking process:

Let a sequence be given as:

3   9    27    81

As can be observed from the sequence, the next number of the sequence is a multiple of 3, that is 9 is a multiple of 3. Similarly, 27 is 9 multiplied by 3

then, let the first term be a. the common multiplying factor will be r (in this case 3). Then the formula will be

In addition, the powers rule applies.

For instance:

9 =

27 =

81 =

Then the explicit formula will be

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step-by-step explanation:

1. x> -5

2. x< 8

step-by-step explanation:

1. 2x> -10

divide by 2 from both sides of equation.

2x/2> -10/2

simplify, to find the answer.

-10/2=-5

x> -5 is the correct answer.

2. 3x< 24

divide by 3 from both sides of equation.

3x/3< 24/3

simplify, to find the answer.

24/3=8

x< 8 is the correct answer.

i hope this you, and have a wonderful day!