Finding Next Term in Arithmetic Sequences

Questions and Answers

What is the next term in the arithmetic sequence 4, 10, 16, 22?

28 (correct)

Which of the following sequences represents a geometric sequence?

2, 4, 8, 16 (correct)

5, 2, 1, 0

9, 7, 5, 3

1, 3, 5, 7

What is the next term in the sequence 3, 9, 27, 81?

162

243 (correct)

100

243 (correct)

In an arithmetic sequence where the first term is 15 and the common difference is -2, what is the fifth term?

7 Signup and view all the answers

What is the next term in the sequence 2, 8, 32, 128?

512 Signup and view all the answers

Which sequence correctly illustrates the use of exponents for the pattern?

1, 2, 4, 8, 16 Signup and view all the answers

In the sequence 5/6, 7/8, 9/10, what is the next term based on the identified pattern?

11/12 Signup and view all the answers

What is the common difference in the arithmetic sequence: 10, 15, 20, 25?

5 Signup and view all the answers

Which sequence must be identified as non-arithmetic and non-geometric?

1, 1/2, 1/3, 1/4 Signup and view all the answers

What is the common ratio in the geometric sequence 7, 21, 63, 189?

3 Signup and view all the answers

Study Notes

Finding the Next Term in a Sequence

A sequence is a list of numbers that follow a specific pattern or rule.
To find the next term in a sequence, identify the pattern or rule that governs the sequence.

Arithmetic Sequences

An arithmetic sequence is a sequence where each term differs from the previous term by a common difference.
To find the next term in an arithmetic sequence, add the common difference to the previous term.
Examples:
- 2, 5, 8, 11, 14 (common difference: 3)
- 5, 9, 13, 17 (common difference: 4)
- 27, 21, 15, 9 (common difference: -6)

Geometric Sequences

A geometric sequence is a sequence where each term differs from the previous term by a common ratio.
To find the next term in a geometric sequence, multiply the previous term by the common ratio.
Examples:
- 3, 6, 12, 24 (common ratio: 2)
- 4, 12, 36 (common ratio: 3)

Other Sequence Patterns

Some sequences may not follow an arithmetic or geometric pattern, but may have other patterns such as exponents (e.g., 1, 4, 9, 16, ...) or fractions (e.g., 3/4, 5/7, 7/10, ...).
To find the next term in such sequences, identify the underlying pattern and apply it to find the next term.

Examples and Applications

Finding the next term in a sequence can be applied to various problems, such as:
- Series of numbers: 2, 5, 8, 11, 14, ...
- Exponents: 1, 4, 9, 16, ...
- Fractions: 3/4, 5/7, 7/10, ...
- Real-world problems: population growth, financial calculations, and more.

Tips and Tricks

When dealing with fractions, separate the numerator and denominator to identify patterns.
Look for patterns in the sequence, such as common differences or ratios.
Use the pattern to find the next term in the sequence.