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