In an Arithmetic Sequence, the diiference between one term and the next one is a constant called the “common difference.”
In general, we could write an Arithmetic Sequence like this:
{, +d, +2d, +3d,…}
where:
is the first term
d is the “common difference”
Example 1: My Arithmetic Sequence: -10, -3, 4, 11, 18, 25. Determine the position of 25 in this sequence.

Know:
= -10 (the first term)
d = 7 (the “common difference”)

We can write an Arithmetic Sequence formula:
= + (n-1).d

Using the Arithmetic Sequence formula:
= + (n-1).d
= -10 + (n-1).7
25 = -10 -7 +7n
25 = -17 +7n
n = 6
Conclusion: 25 is the 6th term
Example 2: My Arithmetic Sequence: -10, -3, 4, 11, 18, 25. Determine

Know: = -10
n = 50
d = 7

Using the Arithmetic Sequence formula:
= + (n-1).d
= -10 + (50-1).7
= 333

To sum up the terms of this Arithmetic Sequence:
+ + +…
= + (+d) + (+2d) +…

Use this formula:

Example 3: Determine the sum of this Arithmetic Sequence: -10, -3, 4, 11, 18, 25

Know:
= -10 (the first term)
d = 7 (the “common difference”)
n = 6 (the number of terms to add up)