Foundation Level (Fail → Pass)

1. What is the difference between an Arithmetic Progression and any other number sequence?

2. Find the first term (a) and the common difference (d) for the sequence 7, 11, 15, 19, ...

3. Using the formula Tₙ = a + (n-1)d, find the 10th term of the sequence 5, 8, 11, ...

4. Explain the difference between the Tₙ formula and the Sₙ formula. What does each one calculate?

5. Find the sum of the first 8 terms of the AP 1, 2, 3, 4, ... using the formula Sₙ = n/2 (a + l).

Intermediate Level (Pass → Credit) 

6. Create a study guide explaining how to find a and d when two terms are given (e.g., the 5th term and the 11th term).

7. The 3rd term of an AP is 10 and the 8th term is 25. Find the first term and the common difference.

8. How many terms are there in the arithmetic progression 6, 10, 14, ..., 62?

9. Find the sum of the first 20 terms of the AP 4, 7, 10, ... using the formula Sₙ = n/2 [2a + (n-1)d].

10. A person saves Rs. 100 in the first month and increases their savings by Rs. 50 each month. How much will they have saved in total after one year?

Advanced Level (Credit → Distinction) 

11. The sum of the first 4 terms of an AP is 36 and the 11th term is 43. Find the first term, common difference, and the sum of the first 15 terms.

12. How many terms of the arithmetic progression 13, 11, 9, ... must be added together for the sum to be 40? Explain why you might get two possible answers.

13. The sum of the first n terms of a series is given by Sₙ = n² - 8n. Find the first term and the common difference of the progression.

14. In an AP, the sum of the 3rd and 6th terms is 42, and the sum of the 2nd and 10th terms is 54. Which term in this progression is 63?

15. A father deposits Rs. 500 in his daughter's bank account on her 10th birthday. Each month after that, he deposits a fixed amount more than the previous month. If the total in the account on her 18th birthday is Rs. 50,400 (without interest), how much was the fixed monthly increase?