Math reviewer

What is an arithmetic sequence?

An arithmetic sequence is a sequence of numbers such that the difference between consecutive terms is constant. This constant difference is called the common difference.

What is the common difference (d) in an arithmetic sequence?

The common difference (d) is the constant value obtained by subtracting any term from its succeeding term. For example, in the sequence a1, a2, a3, \dots, the common difference is d = a2 - a1 = a3 - a_2.

What is the formula for the n^{th} term of an arithmetic sequence?

The formula for the n^{th} term (an) of an arithmetic sequence is given by: an = a_1 + (n-1)d
where:

• a_n is the n^{th} term
• a_1 is the first term
• n is the term number
• d is the common difference.

What is the formula for the sum of the first n terms of an arithmetic sequence?

There are two main formulas for the sum of the first n terms (S_n) of an arithmetic sequence:

1. Given the first term (a1) and the n^{th} term (an):
   Sn = \frac{n}{2}(a1 + a_n)
2. Given the first term (a1) and the common difference (d): Sn = \frac{n}{2}(2a_1 + (n-1)d)

Where:

• S_n is the sum of the first n terms
• n is the number of terms
• a_1 is the first term
• a_n is the n^{th} term
• d is the common difference.