Sequences and Series

The sum of an infinite GP exists when:

1. r > 1
2. r = 1
3. |r| < 1
4. r = 2

A series obtained by adding the terms of a sequence is called:

1. Sequence
2. Series
3. Progression
4. Function

If three numbers are in AP, then the middle term is:

1. Arithmetic mean of the other two
2. Product of the other two
3. Difference of the other two
4. Square of the first term

The arithmetic mean between two numbers a and b is:

1. a+b
2. (a+b)/2
3. ab
4. a-b

If the common ratio of a GP is 1, then the sequence is:

1. Increasing
2. Decreasing
3. Constant
4. Undefined

The sum of the first n terms of a GP is:

1. Sn = a(rⁿ - 1)/(r - 1)
2. Sn = n/2[2a+(n-1)d]
3. Sn = arⁿ
4. Sn = a+r

Find the 5th term of the GP: 2, 6, 18, 54, ...

1. 108
2. 162
3. 216
4. 324

The nth term of a geometric progression is:

1. an = a + (n - 1)d
2. an = arⁿ⁻¹
3. an = n(a+r)
4. an = a/r

The common ratio of the GP: 5, 15, 45, 135 is:

1. 2
2. 3
3. 4
4. 5

Which of the following is a geometric progression?

1. 2, 4, 6, 8
2. 3, 9, 27, 81
3. 5, 10, 15, 20
4. 1, 3, 5, 7

The sum of the first n terms of an arithmetic progression is:

1. Sn = n/2 [2a + (n - 1)d]
2. Sn = a + nd
3. Sn = n(a + d)
4. Sn = a × d

Find the 10th term of the AP: 3, 7, 11, 15, ...

1. 35
2. 39
3. 43
4. 47

The nth term of an arithmetic progression is given by:

1. an = a + nd
2. an = a + (n - 1)d
3. an = n(a + d)
4. an = a × d

Find the common difference of the AP: 7, 12, 17, 22, 27.

1. 3
2. 4
3. 5
4. 6

A sequence in which the difference between consecutive terms is constant is called:

1. Geometric progression
2. Arithmetic progression
3. Harmonic progression
4. Fibonacci sequence