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. The sum of terms is calculated using the average of the first and last terms. The tutorial then introduces geometric sequences, highlighting the common ratio and how each term is derived. The nth term and sum of terms formulas for geometric sequences are also discussed, emphasizing their importance for exams.

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

• 3

• 1

• 4

• 2

How can the second term of an arithmetic sequence be expressed if the first term is 'a' and the common difference is 'd'?

• a / d

• a - d

• a * d

• a + d

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

• a / (n - 1) * d

• a + n * d

• a + (n - 1) * d

• a * n * d

How do you calculate the sum of terms in an arithmetic sequence?

• n * (a + l) / 2

• n * (a - l) / 2

• n * (a + l) * 2

• n * (a - l) * 2

What is the definition of a geometric sequence?

• A sequence with a constant difference

• A sequence with decreasing ratios

• A sequence with a constant ratio

• A sequence with increasing differences

If the first term of a geometric sequence is 'a' and the common ratio is 'r', what is the second term?

• a - r

• a + r

• a / r

• a * r

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

• 5

• 4

• 2

• 3

What is the formula for the nth term of a geometric sequence?

• a + r^n

• a * r^n

• a + r^(n - 1)

• a * r^(n - 1)

How is the sum of terms in a geometric sequence calculated?

• a * (1 - r^n) / (1 - r)

• a * (1 + r^n) / (1 + r)

• a * (1 - r^n) * (1 - r)

• a * (1 + r^n) * (1 + r)

Which of the following is NOT a characteristic of a geometric sequence?

• Multiplicative pattern

• Exponential growth

• Constant difference

• Constant ratio