Properties of AP

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?

1. True

2. 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, $\cdots$ are in A.P. $⟹$ 13$\times$2, 17$\times$2, 21$\times$2, $\cdots$ are also in A.P.

1. False

2. True

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

1. True
2. 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?

1. $9,7,$ and $5$
2. $3,9,$ and $15$
3. $3,7,$ and $11$
4. Both $A$ and $B$
5. None of these

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

1. False
2. 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

1. $10$
2. $11$
3. $12$
4. $noneofthese$

Q.

If a, b, c are in AP then, $a\times b,b^2,c\times b$ are also in AP?

1. False

2. 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

1. $83$
2. $89$
3. $86$
4. $90$

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?

1. True
2. 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, $\cdots$ are in A.P. $⟹$ 13$\times$2, 17$\times$2, 21$\times$2, $\cdots$ are also in A.P.

1. True

2. 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

1. $\{21,25,29\}$, AM $=23$
2. $\{13,17,21\}$, AM $=22$
3. $\{21,25,29\}$, AM $=25$
4. $\{21,22,29\}$, AM $=23$

Q. If $a_1,a_2,a_3,a_4$ are terms of an AP, then the relation between them is

1. $a_1+a_2=a_2+a_3$
2. $a_1+a_4=a_2+a_3$
3. $a_1+a_3=a_2+a_4$

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?

1. True

2. 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.

1. 240
2. 440
3. 260
4. 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

1. $42$
2. $41$
3. $44$
4. $53$