Insertion of AM's Between 2 Numbers

Q.

Insert one arithmetic mean between 3 and 13.

Q.

Insert three arithmetic means between 4 and 12.

1. 7, 9, 11

2. 6, 8, 10

3. 5, 8, 11

4. 4, 8, 12

Q. 12 Derive the formula of arithmetic progression.

Q. Question 1 (ii)
Fill in the blanks in the following table, given that a is the first term, d the common difference and $a_n$ the $n^{th}$ term of the A.P.
$\begin{array}{ccccc}& a& d& n& a_n\\ \left(ii\right)& -18& \dots \dots & 10& 0\end{array}$

Q. Question 30
Find the sum of last ten terms of the AP 8, 10, 12, …., 126.

Q. Question 18
The sum of first five multiples of3 is :

A) 45
B) 55
C) 65
D) 75

Q. Question 13
Find the sum of first 15 multiples of 8.

Q. Question 1
Match the AP’s given in column A with suitable common differences given in column B.
$\begin{array}{cccc}& ColumnA& & ColumnB\\ \left(A_1\right)& 2,-2,-6,-10,....& \left(B_1\right)& \frac{2}{3}\\ \left(A_2\right)& a=-18,n=10,a_n=0& \left(B_2\right)& -5\\ \left(A_3\right)& a=0,a_{10}=6& \left(B_3\right)& 4\\ \left(A_4\right)& a_2=13,a_4=3& \left(B_4\right)& -4\\ & & \left(B_5\right)& 2\\ & & \left(B_6\right)& \frac{1}{2}\\ & & \left(B_7\right)& 5\end{array}$

Q.

20 A.Ms are inserted between 2 and 86. Find the 19th A.M.

1. 84

2. 78

3. 82

4. 80

Q. Question 12
Find the sum of first 40 positive integers divisible by 6.

Q.

The reciprocals of the natural in order give Is it an arithmetic sequence?

Q.

Five arithmetic means are inserted between 6 and 36. Choose the correct numbers among the options.

1. 12

2. 16

3. 26

4. 28

Q.

Which of the following are AP's? If they form an AP, find the common difference d and write three more terms.
(i) −1.2, −3.2, −5.2, −7.2...
(ii)0, -4, −8, −12…
(iii)−$\frac{1}{2}$, −$\frac{1}{2}$, −$\frac{1}{2}$, −$\frac{1}{2}$…
(iv)$\sqrt{2}$, $\sqrt{8}$, $\sqrt{18}$, $\sqrt{32}$…
(v)12, 32, 52, 72…

Q. Arithmetic means between 4 and 12 are and .

1. 6
2. 8
3. 15
4. 5

Q.

Find $x$ if $2x,x+10,3x+2$ are the consecutive terms in an AP.

1. 6

2. 1

3. 9

4. 3

Q. Question 3 (iii)
For the following A.Ps, write the first term and the common difference.
(iii) $\frac{1}{3},\frac{5}{3},\frac{9}{3},\frac{13}{3}\dots \dots$

Q. Three arithmetic terms are inserted between two number a and b. The resulting sequence is a/an ___.

Q.

Subba Rao started work in 1995 at an annual salary of Rs 5000 and received an increment of Rs 200 each year. After how many years did his income reach Rs 7000?

1. 13

2. 10

3. 11

4. 12

Q. Which term of the AP : $3,8,13,18,..$is $78?$

1. $t_{16}$
   
2. $t_{18}$
3. $t_{14}$
4. None of these
   

Q. 20 A.Ms are inserted between 2 and 86. Find the 19th A.M.

Q.

Dividing the natural numbers by 2, we get Is this an arithmetic sequence?

Q.

The second number of and arithmetic sequence is 5. Find the sum of its first and third numbers.

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. For the following A.Ps, write the first term and the common difference.
(i) 3, 1, - 1, - 3 …
(ii) -5, - 1, 3, 7 …

Q. Question 3
For the AP –3, –7, –11, … can we find directly $a_{30}-a_{20}$ without actually finding $a_{30}and{a}_{20}$? Give the reason for your answer.

Q. A contract on construction job specifies a penalty for delay of completion beyond a certain date as follows: ₹ 200 for the first day, ₹ 250 for the second day, ₹ 300 for the third day, etc., the penalty for each succeeding day being ₹ 50 more than for the preceding day. How much money the contractor has to pay as penalty, if he has delayed the work by 30 days?

Q.

A contract on construction job specifies a penalty for delay of completion beyond a certain date as follows: ₹ 200 for the first day, ₹ 250 for the second day, ₹ 300 for the third day, etc., the penalty for each succeeding day being ₹ 50 more than for the preceding day. How much money the contractor has to pay as penalty, if he has delayed the work by 30 days?

1. ₹27750

2. ₹ 28050

3. ₹27500

4. ₹ 28550

Q. Find the sum of first 40 positive integers divisible by 6.

Q. If the nth terms of the two APs: 9, 7, 5, ... and 24, 21, 18, ... are the same, find the value of n.

Q.

Three arithmetic terms are inserted between two number a and b. The resulting sequence is a/an ___?