Q1. The sum of the first 20 odd natural numbers is:
Q2. If the sum of the first $n$ terms of an AP is given by $S_n = 3n^2 + n$, then the second term ($a_2$) is:
Q3. The sum of the first 10 multiples of 5 is:
Q4. Assertion (A): The sum of the first $n$ positive integers is given by $\frac{n(n+1)}{2}$. Reason (R): The positive integers 1, 2, 3, ... form an AP with $a=1$ and $d=1$.
Q5. Find the sum of the AP: 2, 7, 12, ..., to 10 terms.
Solve on white paper.
Q6. Find the sum of the first 1000 positive integers.
Q7. Find the sum of the first 15 multiples of 8.
Q8. How many terms of the AP: 24, 21, 18, ... must be taken so that their sum is 78?
Q9. Find the sum of all odd numbers between 0 and 50.
Q10. The first and the last terms of an AP are 17 and 350 respectively. If the common difference is 9, how many terms are there and what is their sum?
Q11. Case Study: Construction Penalty
A contract on construction job specifies a penalty for delay of completion beyond a certain date as follows: ₹ 200 for the first day, ₹ 250 for the second day, ₹ 300 for the third day, etc., the penalty for each succeeding day being ₹ 50 more than for the preceding day.
(i) What is the penalty for the 10th day?
(ii) How much money the contractor has to pay as penalty, if he has delayed the work by 30 days?
(iii) What is the difference in penalty between the 15th day and the 14th day?