Algebra Part 4 Flashcards
What does S represent in the context of terms?
S is the sum of the terms
In the formula for the sum of roots, what does n represent?
n is the number of terms
What is the formula for the nth term of a Geometric Progression (G.P.)?
an = ar^(n-1)
What is the common ratio in a Geometric Progression?
The fixed number used to multiply each preceding term
What is the formula for the sum of a Geometric Progression (for r < 1)?
S = a1 (1 - r^n) / (1 - r)
What is the formula for the sum of a Geometric Progression (for r > 1)?
S = a1 (r^n - 1) / (r - 1)
What are the methods to solve systems of linear equations?
- Elimination by Substitution
- Elimination by Comparison
- Elimination by Addition or Subtraction
- By Determination or Cramer’s Rule
What is the formula for the Geometric Mean (GM) of a sequence?
GM = (a1 * a2 * a3 * … * an)^(1/n)
True or False: A Harmonic Progression (HP) is a sequence where the reciprocals form an Arithmetic Progression.
True
What is the general form of a Quadratic Equation?
Ax^2 + Bx + C = 0
What is the Quadratic Formula for solving for the roots?
x = (-B ± √(B² - 4AC)) / (2A)
What is the condition for the roots of a quadratic equation to be real and equal?
B² - 4AC = 0
What does B² - 4AC > 0 indicate about the roots of a quadratic equation?
Roots are real and unequal
In proportions, what does the statement ‘ad = bc’ represent?
The product of the extremes equals the product of the means
Fill in the blank: A common difference in an Arithmetic Mean is denoted by _______.
[d]
What is the significance of a homogeneous system in equations?
If the variable terms have the same degree
What is the formula for the sum of an Infinite Geometric Progression?
S = a / (1 - r) for |r| < 1
