The gap between consecutive terms of 3, 7, 11, 15 is 4 and the next term of 2, 6, 10 is 14, so finding the common difference and predicting terms opens this Class 10 progression sheet. Later answers include 2n − 1 for the nth term of the odd numbers and a sum of 25.
Key Takeaways
The common difference of the AP 3, 7, 11, 15 is 4 (Q1).
The next term after 2, 6, 10 is 14 (Q2).
The key gives 2n − 1 as a formula for consecutive odd terms.
Section A: Multiple Choice Questions (1 Mark Each)
6.The sum of the first 5 terms of the AP 1, 3, 5, 7, 9 is
(a) 15(b) 20(c) 25(d) 30
Section B: Short Answer Type Questions (2 Marks Each)
Show all steps clearly.
7.Find the common difference of the AP 10, 7, 4, 1.
8.Write the next two terms of the AP 4, 9, 14.
9.Find the 20th term of the AP 5, 8, 11.
10.Which term of the AP 3, 8, 13, 18 is 78?
11.Find the sum of the first 10 natural numbers.
12.Write the formula for the nth term of an AP with first term a and common difference d.
13.The first term of an AP is 6 and the common difference is 2. Find the sum of the first 4 terms.
14.Find the 11th term of an AP whose first term is 2 and common difference is 3.
Section C: Numericals & Word Problems (3 Marks Each)
Apply the concepts to solve the problems. Show all working.
15.A farmer plants trees in rows such that each row has 2 more trees than the previous row. If the first row has 5 trees, find the number of trees in the 10th row.
16.A person saves ₹100 in the first week and increases his savings by ₹20 every week. Find his total savings after 10 weeks.
17.A clock strikes once at 1 o'clock, twice at 2 o'clock, and so on. Find the total number of strikes in a day (two rounds of 1 to 12).
18.The steps of a staircase rise uniformly. The first step is 15 cm high and the 15th step is 43 cm high. Find the common difference in the rise of successive steps.
19.An athlete runs 1 km on the first day, 2 km on the second day, and increases the distance by 1 km each day. Find the total distance covered in the first 7 days.
20.A company produces 1000 cars in the first year and increases production by 500 cars each year. Find the total production in the first 8 years.
Answer Key
1. b) 4
2. b) 14
3. b) 2n - 1
4. b) 20
5. c) 5, 5, 5, 5
6. c) 25
7. Refer to solution guide.
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End of Worksheet
People Also Ask
What is the common difference of the AP 3, 7, 11, 15?
4, option (b) in this worksheet (Q1).
What comes after 2, 6, 10 in this AP?
14, option (b) in this worksheet (Q2).
What is the nth term of the odd numbers?
2n − 1, from the answer key on this page.
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