The next term of the GP 2, 6, 18, 54 is 162 and the nth term of a GP with first term a and ratio r is arⁿ⁻¹, so this Class 11 sheet opens with one stored term and the general formula. The sum formula a(rⁿ − 1)/(r − 1) appears in the answers.
Key Takeaways
The next term of 2, 6, 18, 54 is 162 (Q1).
The nth term of a GP is arⁿ⁻¹ (Q2).
Q3 records a(rⁿ − 1)/(r − 1) as the GP sum.
Section A: Multiple Choice Questions (1 Mark Each)
Choose the correct option for each question.
1.The next term of the sequence 2, 6, 18, 54 is
(a) 108(b) 162(c) 72(d) 216
2.The nth term of a GP with first term a and common ratio r is
(a) arⁿ(b) arⁿ⁻¹(c) a + (n - 1)d(d) a/rⁿ⁻¹
3.The sum of the first n terms of a GP with first term a and common ratio r (r ≠ 1) is
6.The sum of the infinite GP with first term 6 and common ratio 1/2 is
(a) 6(b) 12(c) 3(d) 18
Section B: Short Answer Type Questions (2 Marks Each)
Show all steps clearly.
7.Write the nth term of a GP with first term a and common ratio r.
8.Find the common ratio of the GP 3, 6, 12, 24.
9.Find the 5th term of the GP 2, 6, 18, ...
10.Write the formula for the sum of the first n terms of a GP (r ≠ 1).
11.Find the sum of the first 4 terms of the GP 2, 4, 8, 16.
12.Write the condition for the sum of an infinite GP to exist.
13.Find the sum of the infinite GP 4, 2, 1, ...
14.Write the 3rd term of a GP whose first term is 1 and common ratio is 3.
Section C: Numericals & Word Problems (3 Marks Each)
Apply the concepts to solve the problems. Show all working.
15.A ball bounces back to 3/4 of its previous height each time. If it is dropped from a height of 4 m, find the total distance it travels before coming to rest.
16.Find the sum of the first 5 terms of the GP 3, 6, 12, 24, ...
17.The first term of a GP is 4 and the common ratio is 2. Find its 6th term.
18.A sum of money doubles every year. If the initial amount is ₹1000, find the amount after 4 years.
19.Find the sum of the infinite GP 1, 1/2, 1/4, 1/8, ...
20.The 2nd term of a GP is 6 and its 3rd term is 12. Find the first term and the common ratio.
Answer Key
1. b) 162
2. b) arⁿ⁻¹
3. a) a(rⁿ - 1)/(r - 1)
4. a) 2
5. b) 16
6. b) 12
7. Refer to solution guide.
8. Refer to solution guide.
9. Refer to solution guide.
10. Refer to solution guide.
11. Refer to solution guide.
12. Refer to solution guide.
13. Refer to solution guide.
14. Refer to solution guide.
15. Refer to solution guide.
16. Refer to solution guide.
17. Refer to solution guide.
18. Refer to solution guide.
19. Refer to solution guide.
20. Refer to solution guide.
End of Worksheet
People Also Ask
What comes after 2, 6, 18, 54?
162, option (b) in this worksheet (Q1).
What is the nth term of a GP?
arⁿ⁻¹, option (b) in this worksheet (Q2).
What is the sum of a GP?
a(rⁿ − 1)/(r − 1), option (a) in this worksheet (Q3).
Stuck on a similar problem? Clear your next doubt instantly with the Doubt Solver.
Browse more free worksheets for CBSE Grade 11.