Arithmetic Sequence and Series

Arithmetic Sequence and Series

By Nicole Stanziale

sequences have patterns using the four operations + - x /

Linear sequences are like lines with that y=mx+b formula you are all familiar with.

notice the pattern between the

y values, when looking at sequences it is like we are only going to look at the y values. We should assume the x values are constant or rewrite the table to make them constant and in numerical order.

here we have the same formula but it is written AN+B.

in sequences we use the letter N to represent what term we are looking at. the first term is when n=1, the second term is when n=2, and so on. think of it like when x=1 on a graph.

we also have special sequence formulas to learn

Multiple Choice

Which of the following is the correct formula in finding the nth term of an arithmetic sequence?

• a_n = a₁ + (n - 1)d

• a_n = a₁ + (n + 1)d

• a_n = a₁ - (n - 1)d

• a_n = a₁ +- (n + 1)d

Multiple Choice

what is the linear equation of sequence 10 15 20 25 ?

• y=5x+5

• y=5x

• y=x+5

• y=5x+1

Multiple Choice

Which of the following is an example of an arithmetic sequence?

• 4, 8, 16, 32, 64

• 1, 2, 4, 7, 11

• 15, 13, 11, 9, 7

• 3, 6, 12, 24, 48

Multiple Choice

It is a sequence wherein the terms are generated by adding a constant number called common difference.

• Arithmetic Sequence

• Fibonacci Sequence

• Geometric Sequence

• Harmonic Sequence

Multiple Choice

Complete the Table.

• 25, 32, 39, 46
• 7, 32, 57, 82
• 32, 39, 46, 53
• 7, 14, 21, 28

Multiple Choice

Write the recursive rule for this situation.

• f(n) = f(n − 1) + 58, n ≥ 2
• f(n) = 58 + 7(n − 1)
• f(n) = 58 − 7(n − 1)
• f(n) = f(n − 1) + 7, n ≥ 2

Multiple Choice

Find f(6) or a₆ for this situation.

• 60
• 160
• 280
• 150

Multiple Choice

What will be the length if there were 20 grocery carts? (Hint: Find explicit rule first)

• 98 inches
• 266 feet
• 266 inches
• 98 feet

Multiple Choice

Which formula defines the sequence

f(1) = 2, f(2) = 6, f(3) = 10, f(4) = 14, f(5) = 18?

• A. f(1) = 2, f(n) = 6 + f(n − 1) for n ≥ 2

• B. f(1) = 2, f(n) = 4 + f(n − 1) for n ≥ 2

• C. f(1) = 2, f(n) = 2 + f(n − 1) for n ≥ 2

• D. f(1) = 6, f(n) = 4 + f(n − 1) for n ≥ 2

Multiple Select

The sum of the terms in a sequence is known as a Series

• True

• False

Multiple Choice

What is the formula for the sum of the first n terms of a geometric sequence?

• $$ar^n$$

• $$ar^{n-1}$$

• $$\frac{a\left(1-r^n\right)}{1-r}$$

• None of these

Multiple Choice

what is the sequence formula of 8 6 4 2 ?

• -2n+10

• -2n

• -2

• 2n-10

Multiple Choice

You are sitting in row 23 and notice there are 65 seats in your row. The row in front of you has 63 seats and the row behind you has 67 seats. There are 42 rows in the auditorium. How many seats does the auditorium contain? (Hint: Find the number of seats in the first and last rows)

• 2,604
• 2,163
• 2,422
• 2,803

Multiple Choice

Evaluate the arithmetic series described:
a₁ = 5, a_n = 145, Find S₁₅

• 1125
• 2255
• 2250
• 2258