30 Questions
What is the nth term formula for the series 1.2.3 + 2.3.4 + 3.4.5 + …..?
n(n+1)(n+2)
What is the common difference of the series 1.2.3 + 2.3.4 + 3.4.5 + …..?
1
How many terms are being selected in the series 1.2.3 + 2.3.4 + 3.4.5 + ….. to find the sum?
n
What is the formula for the sum of an arithmetic series?
(n/2)(2a+(n-1)d)
What is the property of an arithmetic sequence where the mean of the sequence is equal to the sum of the first and last terms divided by 2?
Mean is equal to the sum of the first and last terms divided by 2
What is the common difference of the arithmetic progression 2, 7, 12, 17, 22, …?
5
What is the formula for the nth term of an arithmetic progression?
t_n = a + (n - 1)d
How can you determine if a sequence is an arithmetic progression?
By checking if the difference between each term is constant
What is the pth term of an arithmetic progression?
a + (p - 1)d
What is the representation of an arithmetic progression if 'a' is the first term and 'd' is the common difference?
a, a + d, a + 2d, a + 3d, …
What is the general form of an arithmetico-geometric sequence?
a, (a + d)r, (a + 2d)r^2, ...
What is the formula for the nth term of an arithmetico-geometric sequence?
[a + (n - 1)d]r^(n-1)
What is the formula for the sum of n terms of an arithmetico-geometric sequence when r ≠ 1?
a(1 - r^n) + dr(1 - r^(n-1)) / (1 - r)
What is the condition for the sum of an infinite arithmetico-geometric sequence to exist?
|r| < 1
What is the formula for the sum of an infinite arithmetico-geometric sequence when |r| < 1?
a / (1 - r) + dr / (1 - r)^2
What is a necessary condition for a sequence to be a progression?
The terms of the sequence follow a certain pattern
What can be obtained by adding or subtracting the terms of a sequence?
A series
What is the general term formula for the progression 1, 3, 5, 7, 9, ……..?
Tn = 2n - 1
What are the three main types of progressions?
Arithmetic, geometric, and harmonic
What is a common characteristic of all progressions?
The terms follow a certain pattern
In an arithmetic progression, what is the significance of the common difference?
It is the constant difference between any two consecutive terms.
What is the condition for a sequence to be an arithmetic progression?
The difference between any two consecutive terms is constant.
What is the general term of an arithmetic progression?
an = a + (n - 1)d
How can you determine if a sequence is not an arithmetic progression?
By checking if the difference between consecutive terms is not constant.
What is the significance of the first term and common difference in an arithmetic progression?
They are used to find the general term of the progression.
What is the general term of a geometric progression?
ar^(n-1)
If a, b, c are in geometric progression, what is the relationship between them?
b^2 = ac
What is the formula for the pth term from the end of a finite geometric progression?
ar^(n-p)
What is the condition for a sequence to be a geometric progression?
The ratio of each term to its previous term is constant.
What is the formula for the nth term of a geometric progression?
ar^(n-1)
Test your understanding of arithmetico-geometric progressions, including the general form and nth term of an arithmetico-geometric sequence. Learn how to identify and work with these types of progressions. Review the formulas and concepts related to arithmetico-geometric sequences.
Make Your Own Quizzes and Flashcards
Convert your notes into interactive study material.
Get started for free
