To understand Arithmetic Progression first let us try and recap some other important and related concepts –

1) A succession of numbers formed and arranged according to so definite law is called a sequence.

E.g.: 3, 7, 11, 15…

Or 2, 4, 8, 16…

2) Each number of the sequence is called a term of the sequence. A sequence is said to be finite or infinite according to the number of terms in it i.e. finite or infinite

3) If the terms of a sequence are connected by the sign of (+), we get a series.

E.g.: 3+7+11+15+….

Or 2+4+8+16+….

4) If the terms of a series constantly increase or decrease in numerical value, the series is called a progression. Each of the two series in (3) is a Progression. Read more…

Here we attempt to understand ‘Linear Equations in Two Variables’. To recapitulate, let us first understand what we mean by equating with one variable –

Quick Facts:

• In mathematics, a variable is a value that may change within the scope of a given problem or set of operations.
• In contrast, a constant is a value that remains unchanged, though often unknown or undetermined.
• A real number may be either rational (44 or −29/129) or irrational numbers (pi and square root of 2); either algebraic or transcendental; and either positive, negative or zero. In simpler words, Real numbers can be thought of as points on an infinitely long number line.

Linear Equation in One Variable

If a, b, c are real numbers and x is a variable, then an equation of the type ax + b=c (where a in not equal to 0) is called a linear equation in one variable. On substituting a real number for the variable (x) in a given equation (ax+b), if both the sides of the equation become equal, then the number is called the solution of the equation.

Hence, to solve an equation means to find its solution.

Equivalent Equations

• Two or more equations are said to be equivalent equations when a solution of one equation is also the solution of the other.
• A number which is not a solution of the first is also not the solution of the other.
• Read more…

In this post, we hope to clear up problems that you might have with fractions and their uses in Algebra. Here is a quick overview of the facts to keep in mind while dealing with Ratio and Proportion Questions in SAT Algebra.

What is Ratio?

• A ratio is a comparison of only two numbers or values.
• We generally separate the two numbers in the ratio with a colon (:)
• A fraction is also known as a ratio. Ratios are written as a fraction or with a colon.

Example:

Q: Julie has a basket of  3 marbles, 7 chocolates and 9 pencils. What is the Ratio of chocolates to marbles?

A: Expressed as a fraction, with the numerator equal to the first quantity (chocolates) and the denominator equal to the second (marbles), the answer would be 7/3.  We can write this as 7:3 or say seven to three.

Read more…