Insertion of AP's between 2 Numbers

Q.

Insert 4 A.M.s between 4 and 19.

Q. Which of the following can be insert between $3$ and $19$ as arithmetic means?

1. $7,11,15$
2. $6,8,10$
3. $5,7,9$
4. $4,8,12$

Q.

Insert A.M.s between 7 and 71 in such a way that the 5^th A.M. is 27. Find the number of A.M.s

Q. If $11$ A.M.'s are inserted between $28$ and $10$, then the number of integral A.M.'s is

Q.

Is the sequence root 3 , root 6, root9, root12 , ........... Form an arithmetic progression . give reason.

Q.

For an ap if tm =1/n and tn=1/m then a-d=

Q. If n arithmetic means are inserted between 20 and 80 such that the ratio of first mean to the last mean is 1:3, then the value of n is

1. 10
2. 9
3. 11
4. 12

Q.

How many $3$-letter words with or without meaning, can be formed out of the letters of the word $LOGARITHMS$ if repetition of letters is not allowed?

1. $720$

2. $420$

3. $5040$

4. none of these

Q.

Insert 7 A.M.s between 2 and 17.

Q. How to find the number of arithmetic means between two numbers?

Q.

complete the series

7, 11, 17, 25, 35, 47

Q.

If n A.M.s are inserted between two numbers, prove that the sum of the means equidistant from the beginning and the end is constant.

Q.

Insert six A.M.s between 15 and -13.

Q. 20 arithmetic means are inserted between 2 and 100. The sum of all 20 arithmetic means is

1. 1000
2. 510
3. 1020
4. 500

Q.

There are n A.M.s between 3 and 17. The ratio of the last mean to the first mean is 3 : 1. Find the value of n.

Q. The common difference of the $A.P$. $b_1,b_2,.....b_m$ is $2$ more than the common difference of $A.P$. $a_1,a_2,.....a_n$. If $a_{40}=-159$, $a_{100}=-399$ and $b_{100}=a_{70}$, then $b_1$ is eqaul to

1. $-127$
2. $81$
3. $127$
4. $-81$

Q. A man starts repaying a loan as first instalment of $\text{Rs}.100.$ If he increases the instalment by $\text{Rs}.5$ every month, then what amount he will pay in the ${30}^{th}$
instalment?

Q.

Insert five numbers between 8 and 26 such that the resulting sequence is an A.P.

Q. In a sequence of $21$ terms, the first $11$ terms are in A.P. with common difference $2$ and the last $11$ terms are in G.P. with common ratio $2$. If the middle terms the A.P. is equal to the middle term of the G.P., then the middle term of the entire sequence is

1. $-10/31$
2. $10/31$
3. $32/31$
4. $-31/32$

Q. If $m$ arithmetic means are inserted between $1$ and $31$ so that the ratio of the $7^{th}$ and $(m-1{)}^{th}$ means is $5:9,$ then the value of $m$ is

1. $9$
2. $11$
3. $13$
4. $14$

Q.

If n A.M.s are inserted between 20 and 80 such that first mean:last mean =1:3. Find n

Q. Find the common difference of the A.P created by inserting 20 A.Ms between 2 and 86.

1. 2

2. 3

3. 4

4. 5

Q. If the total revenue received from the sale of $x$ units of a product is, $R\left(x\right)=5x^3+4x^2+8x+12$, then the marginal instantaneous revenue when $x=4$ is _____

Q. Let $X=\{1,2,3,4,5\}$ and $Y=\{1,3,5,7,9\}$ . Which of the following is/are relations from $X$ to $Y$?

1. $R_2=\left\{\right(1,1),(2,1),(3,3),(4,3),(5,5\left)\right\}$
2. $R_1=\left\{\right(x,y):y=2+x,x\in X,y\in Y\}$
3. $R_3=\left\{\right(1,1),(1,3),(3,5),(3,7),(5,7\left)\right\}$
4. $R_4=\left\{\right(1,3),(2,5),(2,4),(7,9\left)\right\}$

Q. If the $n^{th}$ term of an A.P. is $4n+1$, then the common difference, $d$ is equal to

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

Q.

16 A.Ms are inserted between 5 and 50. Find the sum of all the A.Ms.

1. 880

2. 410

3. 440

4. 820

Q. Four arithmetic means are inserted between 9 and 44. Which of the following is/are one of those arithmetic means?

1. 16
2. 23
3. 30
4. 37

Q. If a, b, c are in AP, b -a, c - b and a are in GP, then a : b : c is

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

Q. 100 A.Ms are inserted between 20 and 80. Find the sum of first A.M and last A.M

1. 100

2. 80

3. 60

4. 92

Q. Find the sum of the arithmetic progression : $-26,-24,-22,...$ to $36$ terms.

1. $324$
2. $314$
3. $389$
4. $349$