Arithmetic Progressions

Which statement best summarizes the chapter "Arithmetic Progressions"?

1. Every sequence is an Arithmetic Progression.
2. Arithmetic Progressions involve a constant difference between consecutive terms, and formulas for the nth term and the sum of n terms help solve mathematical and real-life problems efficiently.
3. Arithmetic Progressions always have positive common differences.
4. Arithmetic Progressions can only contain positive numbers.

Which real-life situation can be represented by an Arithmetic Progression?

1. Population doubling every year
2. Daily savings increasing by ₹20 every day
3. Bacteria multiplying by 3 each hour
4. Compound interest growth

The first term of an AP is 8 and the common difference is 6. What is the fifth term?

1. 26
2. 30
3. 32
4. 34

Which formula is used when the last term is known?

1. S_n = (n/2)(a+l)
2. a+(n-1)d
3. 2a+d
4. a+d

If the first term is 12 and the common difference is 0, then the AP is:

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

The sum of the first 10 natural numbers is:

1. 45
2. 50
3. 55
4. 60

What is the 20th term of the AP 6, 10, 14, 18, ...?

1. 78
2. 80
3. 82
4. 84

Which of the following is NOT an Arithmetic Progression?

1. 2, 5, 8, 11
2. 10, 7, 4, 1
3. 6, 12, 18, 24
4. 1, 2, 4, 8

Which term of the AP 4, 9, 14, 19, ... is 49?

1. 8th
2. 9th
3. 10th
4. 11th

Find the common difference of the AP: 15, 11, 7, 3, ...

1. 2
2. -2
3. -4
4. 4

What is the sum of the first n terms of an AP?

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

What is the common difference of the AP: 7, 12, 17, 22, 27?

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

Which of the following is an Arithmetic Progression (AP)?

1. 2, 4, 8, 16, 32
2. 5, 9, 13, 17, 21
3. 1, 4, 9, 16, 25
4. 3, 6, 12, 24, 48

If 10th term is 50 and 1st term is 5, then common difference is:

1. 4
2. 5
3. 6
4. 7

The sum of first 5 terms of AP 1, 3, 5, 7 is:

1. 20
2. 25
3. 30
4. 35

If the nth term of an AP is constant, then the AP is:

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

Which term of AP 7, 13, 19, 25 is 85?

1. 12th
2. 13th
3. 14th
4. 15th

If 1, x, 9 are in AP, then x is:

1. 4
2. 5
3. 6
4. 7

If a, 3a, 5a are in AP, then a is:

1. 0
2. 1
3. Any real number
4. 2

The 20th term of AP 2, 5, 8, 11 is:

1. 57
2. 59
3. 60
4. 62

Which AP has common difference zero?

1. 2, 2, 2, 2
2. 1, 2, 3, 4
3. 3, 5, 7
4. 10, 20, 30

If the 10th term of an AP is 50 and 5th term is 30, common difference is:

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

If a, a + d, a + 2d are in AP, then:

1. d = 0
2. always true
3. a = d
4. cannot be AP

Which term of AP 3, 7, 11, 15 is 39?

1. 8th
2. 9th
3. 10th
4. 11th

The common difference of AP: 12, 9, 6, 3 is:

1. −3
2. 3
3. −6
4. 6

If 7, x, 21 form an AP, then x is:

1. 10
2. 12
3. 14
4. 15

The nth term of AP 5, 10, 15, 20 is:

1. 5n
2. 5n − 5
3. n + 5
4. 10n

Which of the following is an AP?

1. 2, 4, 8, 16
2. 3, 6, 9, 12
3. 1, 4, 9, 16
4. 5, 10, 20, 40