MathematicsClass 10en

📐 Arithmetic Progressions: nth Term and Sum

Master the formulas and applications of arithmetic progressions, including finding the nth term, calculating sums, and solving real-world problems. **What you'll learn:** - Find the nth term of an arithmetic progression using the formula $a_n = a + (n-1)d$ - Calculate the sum of an arithmetic progression using $S_n = \frac{n}{2}(2a + (n-1)d)$ or $S_n = \frac{n}{2}(a + l)$ - Identify the common difference and first term in any sequence - Solve complex problems involving multiple arithmetic progressions - Apply arithmetic progressions to practical scenarios

10 questions · play in your browser

No signup required — try it for free.

Questions in this quiz

Answers hidden — play to find out.

Question 1
What is the common difference in the arithmetic progression $2, 5, 8, 11, 14, ...$ ?
Question 2
In the arithmetic progression $7, 11, 15, 19, ...$ , the first term is $a = ___$ and the common difference is $d = ___$ .
Question 3
Find the 10th term of the arithmetic progression $3, 7, 11, 15, ...$
Question 4
The sequence $5, 10, 15, 20, 25$ is an arithmetic progression with common difference $5$ .
Question 5
Which of the following is NOT an arithmetic progression?
Question 6
Find the sum of the first $20$ terms of the arithmetic progression $2, 4, 6, 8, ...$
Question 7
If the 5th term of an arithmetic progression is $20$ and the common difference is $3$ , what is the first term?
Question 8
An arithmetic progression has first term $a = -10$ and common difference $d = 2.5$ . Which term equals $0$ ?
Question 9
The sum of the first $n$ terms of an arithmetic progression is $S_n = 3n^2 + 2n$ . What is the 3rd term?
Question 10
An arithmetic progression has 15 terms. The first term is $10$ and the last term is $58$ . What is the sum of all terms?