Arithmetic Progressions Quiz

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Questions and Answers

Given the A.P.: $2, 5, 8, ...$, calculate the 10th term.

For the A.P.: $8, 12, 16, ...$, determine the sum of the first 15 terms.

300

If the first term of an A.P. is $7$ and the common difference is $-2$, what is the 25th term?

-41

For the A.P. $4, 10, 16, ...$, what is the common difference?

6 Signup and view all the answers

What is the 5th term of the A.P. defined by $-3, -1, 1, ...$?

5 Signup and view all the answers

Define an arithmetic progression and provide an example.

An arithmetic progression is a sequence where each term is obtained by adding a fixed number, known as the common difference, to the previous term. For example, the sequence 2, 5, 8, 11 is an arithmetic progression with a common difference of 3. Signup and view all the answers

How can the common difference affect the nature of an arithmetic progression?

The common difference can be positive, negative, or zero, which affects whether the sequence is increasing, decreasing, or constant. A positive difference leads to an increasing progression, a negative difference yields a decreasing sequence, and zero results in a constant value for all terms. Signup and view all the answers

Explain how to find the nth term of an arithmetic progression.

The nth term of an arithmetic progression can be found using the formula: $a_n = a + (n-1)d$, where $a$ is the first term, $d$ is the common difference, and $n$ is the term number. Signup and view all the answers

What is the formula for the sum of the first n terms of an arithmetic progression?

The sum of the first n terms of an arithmetic progression is given by the formula: $S_n = \frac{n}{2} (2a + (n - 1)d)$ or equivalently $S_n = \frac{n}{2}(a + a_n)$, where $a$ is the first term, $d$ is the common difference, and $a_n$ is the nth term. Signup and view all the answers

Discuss the implications of having a zero common difference in an arithmetic progression.

A zero common difference indicates that all terms in the arithmetic progression are identical, resulting in a constant sequence, such as 5, 5, 5, 5. This specialization limits variability and often simplifies calculations and analysis. Signup and view all the answers

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Study Notes

Arithmetic Progressions

An arithmetic progression (AP) is a sequence where each term, except the first, is obtained by adding a fixed number to the preceding term.
The fixed number added in an AP is called the common difference.
The common difference in an AP can be positive, negative, or zero.
Many questions involve finding the common difference in a given AP sequence.
Other questions require finding the nth term of the sequence.
You may also be asked to find the sum of terms of an AP.
The questions are presented in a multiple-choice format with answers labeled (a), (b), (c), and (d).
The total number of questions in the image is 59.
The image contains questions that require you to apply arithmetic progression concepts to various sequences with different common differences and starting values.