Explicit Formulas and Sequences

The video tutorial explains how to identify and write explicit formulas for arithmetic sequences. It begins with an introduction to arithmetic sequences, highlighting the concept of a common difference. The tutorial then demonstrates how to write explicit formulas using the first term and common difference. Two examples are provided: one with a positive common difference and another with a negative common difference. The video also includes verification of the explicit formulas by substituting sequence terms.

What is the common difference in the sequence 12, 22, 32, 42?

• 8

• 14

• 10

• 12

How do you identify if a sequence is arithmetic?

• By checking if the terms are increasing

• By checking if the terms are prime numbers

• By checking if the terms are decreasing

• By checking if there is a constant difference between consecutive terms

What is the first term of the sequence 12, 22, 32, 42?

• 10

• 12

• 22

• 32

Which formula represents the explicit formula for an arithmetic sequence?

• a_n = a_1 + d(n + 1)

• a_n = a_1 + d(n - 1)

• a_n = a_1 - d(n - 1)

• a_n = a_1 + d(n)

What is the explicit formula for the sequence 12, 22, 32, 42?

• a_n = 10n + 2

• a_n = 10n + 12

• a_n = 12n + 10

• a_n = 10n - 2

What is the simplified form of the expression 10(n - 1) + 12?

• 10n - 12

• 10n + 2

• 10n - 2

• 10n + 12

How do you verify the explicit formula for a sequence?

• By checking if it matches the first term only

• By checking if it matches the last term only

• By substituting values of n and checking if it matches known terms

• By checking if it matches the sum of all terms

What is the value of a_1 using the explicit formula a_n = 10n + 2?

• 10

• 12

• 22

• 32

What is the value of a_4 using the explicit formula a_n = 10n + 2?

• 52

• 62

• 42

• 32

What is the common difference in the sequence 55, 48, 41, 34?

• -8

• -7

• -6

• -5