Q1. If the sum of the first $n$ terms of an AP is $S_n = 3n^2 + n$, then its common difference is:
Q2. The 4th term from the end of the AP: -11, -8, -5, ..., 49 is:
Q3. If 7 times the 7th term of an AP is equal to 11 times its 11th term, then its 18th term will be:
Q4. Two APs have the same common difference. The difference between their 100th terms is 100, what is the difference between their 1000th terms?
Q5. Assertion (A): The sum of the series 1 + 3 + 5 + ... + 19 is 100. Reason (R): Sum of first $n$ odd natural numbers is $n^2$.
Q6. Find the middle term of the AP: 6, 13, 20, ..., 216.
Solve on white paper.
Q7. Which term of the AP: 3, 15, 27, 39, ... will be 132 more than its 54th term?
Q8. Find the sum of all two digit numbers which when divided by 3 yield 1 as remainder.
Q9. If the sum of first 7 terms of an AP is 49 and that of 17 terms is 289, find the sum of first $n$ terms.
Q10. A sum of ₹ 700 is to be used to give seven cash prizes to students of a school for their overall academic performance. If each prize is ₹ 20 less than its preceding prize, find the value of each of the prizes.
Q11. Case Study: Potato Race
In a potato race, a bucket is placed at the starting point, which is 5 m from the first potato, and the other potatoes are placed 3 m apart in a straight line. There are 10 potatoes in the line.
(i) What is the distance covered by the competitor to pick up the 1st potato and put it in the bucket?
(ii) What is the distance covered for the 2nd potato?
(iii) What is the total distance the competitor has to run?
Q12. Case Study: Ladder Rungs
A ladder has rungs 25 cm apart. The rungs decrease uniformly in length from 45 cm at the bottom to 25 cm at the top. The top and the bottom rungs are $2 \frac{1}{2}$ m apart.
(i) Find the number of rungs.
(ii) What is the length of the middle rung (or average length)?
(iii) What is the total length of the wood required for the rungs?