Geometric and Arithmetic Sequences

The video tutorial covers arithmetic and geometric sequences, explaining how to find the nth term and the sum of terms for each type. It begins with arithmetic sequences, defining the nth term using the first term and common difference, and then explains how to calculate the sum of terms using averages. The tutorial then introduces geometric sequences, highlighting the common ratio and how to determine the nth term and sum of terms. Key formulas for both sequence types are emphasized for exam preparation.

What is the common difference in the sequence 3, 5, 7, 9?

• 1

• 2

• 3

• 4

How can the nth term of an arithmetic sequence be expressed?

• a * d

• a + n

• a + (n - 1) * d

• a + n * d

Which of the following is NOT a characteristic of an arithmetic sequence?

• Evenly spaced terms

• Linear pattern

• Constant ratio

• Constant difference

What is the formula for the sum of terms in an arithmetic sequence?

• n * (a + l) / 2

• a + n * d

• n * (a + d)

• a * n

What defines a geometric sequence?

• Common difference

• Common ratio

• Common sum

• Common product

How is the nth term of a geometric sequence expressed?

• a * n

• a + r

• a * r^(n-1)

• a * r

What is the common ratio in the sequence 3, 9, 27, 81?

• 2

• 3

• 4

• 5

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

• a * r^n

• a + r^n

• a * (1 - r^n) / (1 - r)

• a * n

What is the key difference between arithmetic and geometric sequences?

• Both have common differences

• Arithmetic has a common difference, geometric has a common ratio

• Arithmetic has a common ratio, geometric has a common difference

• Both have common ratios

For exam preparation, which concepts are crucial to understand?

• Neither arithmetic nor geometric sequences

• Only arithmetic sequences

• Only geometric sequences

• Both arithmetic and geometric sequences