Question

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Dino and Jessica were doing their homework when Dino got to a problem about sequences that only had the numbers 2, 4, . . . written down. Dino thought this was an arithmetic sequence while Jessica was sure it was geometric.

a. If Dino was right, find the next 3 terms of the sequence and the rule. Create an equation that represents the situation.

b. If Jessica is right, find the next three terms of the sequence and the rule. Create an equation that represents the situation

c. Jessica found in her notes the number 128 is an output of the sequence. Is the sequence arithmetic or geometric? How do you know?

Answer 1

Explanation:

Start of the sequence:

• 2, 4, ...

a) Dino

Arithmetic sequence, with the common difference of 2, next 3 terms will be:

• 6, 8, 10

a(n) = 2n would be an equation for the nth term

b) Jessica

Geometric sequence, with common ratio of 2, next 3 terms are:

• 8, 16, 32

a(n) = 2ⁿ would be an equation of the nth term.

c)

Both sequences have same term of 128:

• 2n = 128 ⇒ n = 64
• 2ⁿ = 128 ⇒ n = 7