# Properties of AP

## Trending Questions

**Q.**

A fruit seller was fond of mathematics. He always kept his stock fruits in AP. One day he had 2 apples, 4 bananas, and 6 mangoes. A thief took 2 from each of the fruits. Are the number of fruits of each type in an AP?

True

False

**Q.**

**Question 7 (iv)**

In which of the following situations, do the lists of numbers involved form an AP? Give reasons for your answers.

The number of bacteria in a certain food item after each second, when they double in every second.

**Q.**Question 1 (iv)

Which of the following form an AP? Justify your answer.

11, 22, 33, ….

**Q.**

13, 17, 21, ⋯ are in A.P. ⟹ 13×2, 17×2, 21×2, ⋯ are also in A.P.

False

True

**Q.**The sequence 1, 3, 6, 9 is in AP

- True
- False

**Q.**Find three numbers in AP whose sum is 15 and product is 80.

**Q.**An AP starts with a positive fraction and every alternate term is an integer. If the sum of the first 11 terms is 33, then find the 4th term

**Q.**The sum of the three numbers in A.P is 21 and the product of the first and third number of the sequence is 45. What are the three numbers?

- 9, 7, and 5
- 3, 9, and 15
- 3, 7, and 11
- Both A and B
- None of these

**Q.**The sequence of numbers 5, - 2, -9, -16, ... is an AP with common difference -7.

- False
- True

**Q.**Three numbers are in AP such that their sum is 18 and sum of their squares is 158. The greatest number among them is

- 10
- 11
- 12
- none of these

**Q.**

If a, b, c are in AP then, a×b, b2, c×b are also in AP?

False

True

**Q.**The mean of five numbers in AP is 89. The product of first and last terms is 7885. The AM of first, third and fifth term is

- 83
- 89
- 86
- 90

**Q.**A fruit seller was fond of mathematics. He always kept his stock fruits in AP. One day he had 2 apples, 4 bananas and 6 mangoes. A thief took 2 from each of the fruits. Are the number of fruits of each type in an AP?

- True
- False

**Q.**The sum of three numbers in A.P. is 21 and the sum of their squares is 197. Find the middle number.

**Q.**

If (2p+1), 13, (5p−3) are in AP, find the value of p.

**Q.**

13, 17, 21, ⋯ are in A.P. ⟹ 13×2, 17×2, 21×2, ⋯ are also in A.P.

True

False

**Q.**The Sum of three numbers in AP is 75, and product of extremities is 609. The AM of first and second number is

- {21, 25, 29}, AM =23
- {13, 17, 21}, AM =22
- {21, 25, 29}, AM =25
- {21, 22, 29}, AM =23

**Q.**If a1, a2, a3, a4 are terms of an AP, then the relation between them is

- a1+a2=a2+a3
- a1+a4=a2+a3
- a1+a3=a2+a4

**Q.**

A fruit seller was fond of mathematics. He always kept his stock fruits in AP. One day he had 2 apples, 4 bananas, and 6 mangoes. A thief took 2 from each of the fruits. Are the number of fruits of each type in an AP?

True

False

**Q.**8 terms are inserted between 5 and 43 so that the resulting sequence is an AP. The sum of the resulting AP is

- 240
- 440
- 260
- 280

**Q.**The sum of four numbers in AP is 176. The product of 1st and last is 1855. The mean of middle two is

- 42
- 41
- 44
- 53