Arithmetic Sequence: The Adventure

An arithmetic sequence is an ordered set of numbers that have a common difference between each consecutive term. There is common difference in this sequence.

​Common difference

If the difference between every pair of consecutive terms in a sequence is the same, this is called the common difference. For example, the sequence 4,7,10,13,... has a common difference of 3. A sequence with a common difference is an arithmetic progression.

d = 5 - 2
= 3
Therefore the common difference is 3.

​Solution:

Ex. "In the sequence 2, 5, 8, 11, ...
Given:
a₂ = 5
a₁ = 2

​d = a_n - a_n-1

d = 40 - 30
= 10
Therefore the common difference is 10.

​Solution:

Ex. "In the sequence 10, 20, 30, 40
Given:
a₄ = 40
a₃ = 30

​d = a_n - a_n-1

​Formula: a_n= a + (n - 1) d

Where:

a_n = n^th term of the arithmetic sequence.
a = the first term of the arithmetic sequence.
n = is the position of the term you want to find.
d = Common difference

 a₅ = a₁ + (5 - 1) 3
= -6 + 4 * 3
= -6 + 12
= 6

The 5th term in this sequence is 6.

Solution:

Given:
 a₁ = -6

d = 3
Find the a₅

Example: -6, -3, 0, 3, __

 a₈ = -6 + (8 - 1) 3
= -6 + 7 * 3
= -6 + 21
= 15

The 8th term in this sequence is 15.

Solution:

a₁ = -6

d = 3

Given: