Sequences: Do Now

What is the formula for the nth term of an arithmetic sequence?

• a_n = a_1 + (n+1)d

• a_n = a_1 + (n-1)c

• a_n = a_1 + (n-1)d

• a_n = a_1 - (n-1)d

In a geometric sequence, what is the common ratio between consecutive terms?

• The common ratio in a geometric sequence changes with each term

• The common ratio in a geometric sequence is equal to the sum of the terms

• The common ratio between consecutive terms in a geometric sequence is a constant value.

• The common ratio in a geometric sequence is always negative

Give an example of an explicit formula for a geometric sequence.

• a_n = a_1 + r^(n-1)

• a_n = a_1 * r^(n-1)

• a_n = a_1 + r^n

• a_n = a_1 * r^n

Explain the difference between an explicit formula and a recursive formula for a sequence.

• An explicit formula and a recursive formula both provide the nth term directly.

• An explicit formula and a recursive formula both define the nth term based on previous terms.

• An explicit formula provides the nth term directly, while a recursive formula defines the nth term based on previous terms.

• An explicit formula defines the nth term based on previous terms, while a recursive formula provides the nth term directly.

If the first term of an arithmetic sequence is 3 and the common difference is 5, what is the 10th term?

• 48

• 35

• 52

• 60

For a geometric sequence with a first term of 2 and a common ratio of 3, what is the 5th term?

• 12

• 45

• 162

• 81

How can you determine if a sequence is arithmetic or geometric?

• Check if the difference between consecutive terms is constant for arithmetic sequence, and check if the ratio between consecutive terms is constant for geometric sequence.

• Check if the product of terms is constant for geometric sequence

• Check if the sum of terms is constant for arithmetic sequence

• Check if the terms are all prime numbers

What is the sum of the first 10 terms of an arithmetic sequence with a first term of 1 and a common difference of 2?

• 120

• 50

• 100

• 75

The graph of an arithmetic sequence is ​ ​ (a)   and the graph of a geometric sequence is ​ (b)   .

• linear
• exponential

Given the recursive formula, find the first four terms:
a_n = a_n-1 + 5
a₁ = -16

• -16, -21, -26, -31
• 5, -11, -27, -43
• -16, -80, -500, -200
• -16, -11, -6, -1