Unit 1 - Practice Quiz

1 A sequence of numbers is called an Arithmetic Progression (AP) if the difference between any two consecutive terms is:

2 Which of the following represents the -th term () of an Arithmetic Progression with first term and common difference ?

3 In a Geometric Progression (GP), the ratio of any term to its preceding term is called the:

4 Which of the following is the formula for the -th term of a Geometric Progression?

5 Three non-zero numbers are in Harmonic Progression (HP) if:

6 Find the 10th term of the AP:

7 What is the sum of the first natural numbers?

8 If are in Arithmetic Progression, which relation holds true?

9 Find the common ratio of the GP:

10 The sum of an infinite Geometric Progression exists only if the common ratio satisfies:

11 Calculate the sum of the infinite GP:

12 If , , and are the Arithmetic, Geometric, and Harmonic means of two distinct positive numbers, which inequality is correct?

13 What is the Geometric Mean (GM) of the numbers 4 and 16?

14 What is the Arithmetic Mean (AM) of the numbers 4 and 16?

15 The formula for the Harmonic Mean (HM) of two numbers and is:

16 Which relation connects the Arithmetic Mean (A), Geometric Mean (G), and Harmonic Mean (H) of two numbers?

17 Identify the type of progression:

18 Identify the type of progression:

19 Find the sum of the first 20 terms of the AP:

20 If are in Arithmetic Progression, find the value of .

21 What is the 5th term of the GP: ?

22 The sum of the first terms of a GP where is given by:

23 If every term of an AP is multiplied by a non-zero constant , the resulting sequence is:

24 If every term of a GP is raised to the power 2, the resulting sequence is:

25 Which term of the AP is 81?

26 What is the common difference of the AP whose -th term is given by ?

27 Find the Harmonic Mean of 3 and 6.

28 Which of the following sequences can never contain the term 0?

29 What is the 7th term of the HP: ?

30 The sum of the first odd natural numbers is:

31 If are in GP, then are in:

32 Find if are in Geometric Progression.

33 The recurring decimal can be expressed as a sum of an infinite GP. The common ratio is:

34 If the sum of three numbers in AP is 15, the middle term is:

35 Which of the following is NOT an Arithmetic Progression?

36 Find the sum of the series: to terms. (General approach)

37 If are in Harmonic Progression, then is called the:

38 What is the 8th term of the sequence defined by ?

39 Insert two Arithmetic Means between 5 and 11.

40 If the -th term of a GP is , what is the first term ?

41 In an AP, if , find the first term .

42 The product of three numbers in a Geometric Progression is 216. Find the middle term.

43 If and for two numbers, find their .

44 Which of the following is true for the sequence ?

45 Find the value of .

46 If denotes the sum of terms of an AP with common difference , then equals:

47 If positive numbers are in HP, then:

48 The sum of the first even natural numbers () is:

49 Which term of the AP is -81?

50 If the 3rd term of a GP is 4, find the product of its first 5 terms.