Exploring Arithmetic Progressions in Mathematics

The constant increment or decrement between consecutive terms.

S_n = \frac{n}{2}(a_1 + a_n)

Loan repayment: Fixed monthly payments to pay off a loan with a constant interest rate.

<p>With the common difference representing the annual increase in the population.</p> Signup and view all the answers

<p>Paint peeling: If paint peels away from a wall at a constant rate each day.</p> Signup and view all the answers

<p>a_n = a_1 + (n-1)d</p> Signup and view all the answers

<p>The common difference in an arithmetic progression is the fixed value by which each term increases or decreases. It determines the pattern and spacing between every pair of consecutive terms.</p> Signup and view all the answers

<p>The sum of n terms in an arithmetic progression is found using the formula: $S_n = \frac{n}{2}[2a_1 + (n - 1)d]$, where $n$ is the number of terms, $a_1$ is the first term, and $d$ is the common difference.</p> Signup and view all the answers

<p>Arithmetic progressions are commonly used in financial planning to calculate savings growth over time. For instance, when determining compound interest or regular investments, the concept of APs helps in predicting future values.</p> Signup and view all the answers

<p>The formula to find the nth term of an arithmetic progression is given by $a_n = a_1 + (n - 1)d$, where $a_n$ is the nth term, $a_1$ is the first term, $d$ is the common difference, and $n$ is the position of the desired term.</p> Signup and view all the answers

<p>The 10th term of the AP with a first term of 5 and a common difference of -2 is -15.</p> Signup and view all the answers