Mathematics 3: Arithmetic Sequences and Series

The common difference of an arithmetic sequence is always 1.

The formula an = a1 + (n - 1)d is used to find the nth term of a geometric sequence.

If ap and aq are two non-consecutive terms in an arithmetic sequence, then ap = aq.

The common difference of an arithmetic sequence can be found by subtracting the first term from the last term.

The arithmetic sequence {a1, a1 + d, a1 + 2d,...} is an infinite sequence.

The nth term of an arithmetic sequence can be found using the formula an = a1 - (n - 1)d.

The common difference of an arithmetic sequence is the average of two consecutive terms.

If a1 = 2 and d = 3, then the 5th term of the arithmetic sequence is 14.

The formula an = a1 + (n - 1)d is used to find the first term of an arithmetic sequence.

An arithmetic sequence can be represented as {a1, a1 + d, a1 + 2d,...} or as a1, a1 + d, a1 + 2d,....