Arithmetic Progressions

An arithmetic progression is a series of numbers whose consecutive difference ? is added to the preceding number, in which the numbers have the form:

(A01)

(A02)

?  =  sum of arithmetic progression<i class="emphasis">n</i>  =  number of terms in arithmetic progression<i class="emphasis">a</i>  =  first number in arithmetic progression<i class="emphasis">z</i>  =   final number in arithmetic progression<span class="unicode">?</span> =   common difference between consecutive numbers. When <span class="unicode">?</span> > 0 theprogression increases; when <span class="unicode">?</span> < 0 the progression decreases.

Geometric Progressions

A geometric progression is a series of numbers whose consecutive difference is a ratio r of the preceding number, in which the numbers have the form:

(A03)

(A04)

? = sum of geometric progression<i class="emphasis">a</i> = first number in geometric progression<i class="emphasis">z</i> = final number in geometric progression<i class="emphasis">r</i> = common ratio between consecutive numbers. When <i class="emphasis">r</i> > 1 the progressionincreases; when <i class="emphasis">r</i> < 1 the progression decreases.<i class="emphasis">n</i> = number of terms in geometric progression

Exponential Relations

Quadratic Equation

(A05)

Binomial Theorem

Square of a Polynomial

The square of a polynomial equals the sum of the squares of each term plus twice the products of each pair of terms, as follows:

Thus

Logarithms

A logarithm is the inverse of an exponential. For example, the equation x = a ^y can be written as y = log _a x, which means y is the logarithm to the base