- Tables, Graphs, Functions and Sequences
- Making a table and plotting points given a unit rate
- Graphing whole number functions
- Function tables with two-step rules
- Writing a function rule given a table of ordered pairs: One-step rules
- Graphing a line in quadrant 1
- Interpreting a line graph
- Finding outputs of a one-step function that models a real-world situation
- Finding outputs of a two-step function with decimals that models a real-world situation
- Writing and evaluating a function that models a real-world situation: Basic
- Graphing ordered pairs and writing an equation from a table of values in context
- Writing an equation and drawing its graph to model a real-world situation: Basic
- Identifying independent and dependent quantities from tables and graphs
- Finding the next terms of an arithmetic sequence with whole numbers
- Finding the next terms of a geometric sequence with whole numbers
- Finding patterns in shapes
- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who
Finding the next terms of an arithmetic sequence with whole numbers
A sequence is a set or series of numbers that follow a certain rule.
For example −
1, 3, 5, 7… is a sequence of numbers that follow a rule: To find a number in this sequence we add 2 to the previous number.
An Arithmetic sequence is a series of numbers where each number is found by adding or subtracting a constant from the previous number.
The constant in an arithmetic sequence is known as the common difference ‘d’.
In general, we write an arithmetic sequence as follows…
a, a + d, a + 2d , a + 3d, a + 4d…
where, a is the first term and d is the common difference.
The rule for finding nth term of an arithmetic sequence
an = a + (n−1)d
an is the nth term, d is the common difference.
The first three terms of an arithmetic sequence are 13, 18, and 23. Find the next two terms of this sequence.
Given the arithmetic sequence 13, 18 and 23. The common difference is
18 −13 = 23 −18 = 5 or d = 5
The next two terms in the sequence are 23 + 5 and 28 + 5 or 28 and 33
So the answer is 28 and 33
The first three terms of an arithmetic sequence are 11, 4, and −3. Find the next two terms of this sequence.
Given the arithmetic sequence 11, 4 and −3. The common difference is
4 −11 = −3 − 4 = −7 or d = −7
The next two terms in the sequence are −3 −7 and −10 −7 or −10 and −17
So the answer is −10 and −17