Geometric Explicit Equation

Geometric Explicit Equation

Using exponents to find any term in the sequence

Exponent

• Tells us how many times to multiply the number

• On your calculator the exponent button may be x^y or yⁿ or a^b

• It will have an exponent variable

• On your calculator (phone or chromebook or calculator) find your exponent button

Let´s try it out

Follow the instructions

What answer do you get?

You should get 60,466,176

Let´s try it out again

Follow the instructions

What answer do you get?

You should get 1,283,918,464,548,864

Let´s try it out with multiplication

Follow the instructions

What answer do you get?

You should get 5,368,709,120

Let´s try it out again with multiplication

Follow the instructions

What answer do you get?

You should get 23,944,605,696

Practice Using Geometric Explicit Equations

Follow the instructions

What answer do you get?

You should get 80,621,568

Multiple Choice

Write the explicit formula for the sequence given by 3, 6, 12, 24, …

• f(n)= 3(2)^n-1

• f(n)= 3+(2)ⁿ

• f(n)= 3(2)ⁿ

• f(n)= 3+(2)^n-1

Open Ended

If the equation is f(n) = 3(2)^n-1 then what is f(13) the 13th term?

Multiple Choice

Find the first four terms of the sequence given the rule:

f(n) = 4(5)^n-1

• 20, 100, 500, 2500

• 5, 20, 80, 320

• 4, 20, 100, 500

• 4, 9, 14, 19

Multiple Choice

Which sequence is represented by the equation f(n) = 2(7)^n-1 ?

• 7, 14, 28, 56...

• 2, 14, 98, 686...

• 2, 9, 16, 23...

• 7,9,11,13...

Multiple Choice

Write an explicit rule for the general term of the sequence 5, 15, 45, . . . ?

• f(n) = a_n-1 x 3

• f(n) = 5(3)^n-1

• f(n) = 3(5)^n-1

• f(n) = 5 + (n-1)3

Multiple Choice

What is the explicit rule for the sequence:

11, 22, 44, 88...

• f(n) = 2(11)^n-1

• f(n) = 11x 2

• f(n) = 11(2)^n-1

• f(n) = 2a_n-1