Arithmetic Progressions Quiz

29

300

-41

<p>6</p> Signup and view all the answers

<p>5</p> Signup and view all the answers

<p>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.</p> Signup and view all the answers

<p>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.</p> Signup and view all the answers

<p>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.</p> Signup and view all the answers

<p>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.</p> Signup and view all the answers

<p>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.</p> Signup and view all the answers