Sequences -Remote -1/25/2023

Write the explicit formula for the following geometric sequence:

3, -12, 48, -192, ...

• a_n = 4(3)^n-1

• a_n = 3(4)^n-1

• a_n = -4(3)^n-1

• a_n = 3(-4)^n-1

Select any statement that is true concerning the sequence 5, 10, 20, 40, 80...

• The sequence is arithmetic

• The sequence is geometric

• The explicit formula is a_n = 5(2)^n-1

• The sequence can be modeled by a linear function.

• The sequence can be modeled by an exponential function.

Is the sequence-4, -12, -36, -108,... geometric?

• yes
• no

Find the common ratio: 4, -16, 64, -256, ...

• r = -4
• r = 2
• r = -2
• r = 4

You have $729 in the bank on Day 1, $243 on Day 2, and $81 on Day 3. Write the explicit formula that expresses the sequence.

• a_n = 729(1/3)^n-1

• a_n = 729(3)^n-1

• a_n = 1/3(a_n-1)

• a_n = 1/3(729)^n-1

Write the recursive rule for the geometric sequence:
64, 16, 4,...

• a₁ = 64; a_n = a_n-1 - ¼
• a₁ = 4; a_n = 4(a_n-1)
• a₁ = 64; a_n = 4(a_n-1)
• a₁ = 64; a_n =   1/4(a_n-1)

Find the first four terms of the sequence given the rule:
a₁ = 10: a_n = a_n-1(3)

• 3, 9, 27, 81
• 10, 30, 90, 270
• 10, 13, 16, 19
• 30, 90, 270, 810

What is the equation for this sequence: 15,45,135,405...

• t(n) = 3(5)ⁿ

• t(n) = 15(3)ⁿ

• t(n) = 5(3)ⁿ

• t(n) = 15(5)ⁿ

What is the equation for this sequence: 1024, 256, 64...

• t(n) = 1024(0.5)ⁿ

• t(n) = 4096(0.5)ⁿ

• t(n) = 4096(0.25)ⁿ

• t(n) = 1024(0.25)ⁿ

What is the equation for this sequence: 1160, 80, 40, 20...?

• t(n) = 2320(0.25)ⁿ

• t(n) = 1160(0.5)ⁿ

• t(n) = 2320(0.5)ⁿ

• t(n) = 1160(0.25)ⁿ