Arithmetic and Geometric Sequences

The video tutorial covers chapter 8 quiz review, focusing on sequence questions, both arithmetic and geometric. It explains how to write the first six terms of a sequence, find the sum of a series, and determine whether a sequence is arithmetic or geometric. The tutorial also covers writing rules for the nth term and using summation notation, with practical applications like stamp collection and flower growth.

What is the first term of the arithmetic sequence if the rule is given by a_n = 2n + 3?

• 2

• 3

• 7

• 5

How do you find the sum of the series 1, 4, 9, 16, 25?

• Divide all terms

• Subtract all terms

• Multiply all terms

• Add all terms

Which of the following sequences is geometric?

• 2, 4, 6, 8

• 7, 14, 21, 28

• 3, 6, 12, 24

• 5, 10, 15, 20

What is the common difference in the sequence 5, 10, 15, 20?

• 2

• 3

• 4

• 5

If a sequence is defined by a_n = 4n - 3, what is the 5th term?

• 23

• 21

• 19

• 17

How many terms are there in the arithmetic sequence starting at 3 and increasing by 5 until 53?

• 10

• 11

• 13

• 12

What is the rule for the nth term of an arithmetic sequence with a first term of 7 and a common difference of 3?

• a_n = 7n - 3

• a_n = 7n + 3

• a_n = 3n + 7

• a_n = 3n + 4

What is the 7th term of the geometric sequence defined by a_n = 3 * 2^(n-1)?

• 192

• 768

• 96

• 384

What is the sum of the first 5 terms of the sequence defined by a_n = 2^n?

• 33

• 32

• 34

• 31

In a geometric sequence, if the first term is 5 and the common ratio is 2, what is the 4th term?

• 40

• 80

• 20

• 160