Arithmetic Mean

Q.

Find the value of x for which (8x+4), (6x-2) and (2x+7) are in A.P.

Q.

If ⁿP₄ = 12 ⁿP₂ the find n.

Q.

If $a_3=15,S_{10}=125$, find $d$ and $a_{10}$

Q.

If x+1, 3x and 4x+2 are in A.P., find the value of x.

Q. Question 12
Split 207 into three parts such that these are in AP and the product of the two smaller parts is 4623.

Q. if 0.7 bar =p/q , then p+q = ?

Q. Sum of 1 to n natural numbers is 36, then find the value of n .

Q.

There are four children A, B, C and D. A has 6 chocolates, B has 7 chocolates, C has 8 chocolates and D has 11 chocolates. Who has the average number of chocolates?

1. A

2. B

3. C

4. D

Q.

If an= 5-11n, then find the common difference

Q. If the numbers x − 2, 4x − 1 and 5x + 2 are in A.P. find the value of x.

Q.

Find the arithmetic mean of :

(i) -5 and 41

(ii) 3x - 2y and 3x + 2y

(iii) $(m+n^2)and(m-n{)}^2$

Q.

The same value of x satisfies the equations 4x + 5 = 0 and 4x²+ (5 + 3p)x + 3p²=0, then p is

1. 0 or 1/4

2. 0 or 5/4

3. 1/4 or 1/2

4. 0 or 1/2

Q. The arithmetic mean (average) of a set of $50$ numbers is $38$. If two numbers, namely, $45$ and $55$, are discarded, the mean of the remaining set of numbers is :

1. $36.5$
2. $37$
3. $37.2$
4. $37.5$
5. $37.52$

Q. 64.A person wrote 15 numbers on a circle. Each number was the arithmetic mean of its two neighbours. If one of these numbers was 6, then the sum of all the numbers written on the circle is (1) 120 (2) 189 (3) 100 (4) 90

Q. Find the arithmetic mean of the AP $2,4,6,8,...20.$

1. 9
2. 10
3. 10.5
4. 11

Q. Find the arithmetic mean of the AP $2,4,6,8,...20.$

1. 9
2. 10
3. 10.5
4. 11

Q.

$\frac{1}{a},\frac{1}{b},and\frac{1}{c},$ are in A. P. show that : bc , ca and ab are also in A.P.

Q. Question 2
In an AP, if a = 3.5, d = 0 and n = 101, then $a_n$ will be:

A) 0
B) 3.5
C) 103.5
D) 104.5

Q. If $\frac{(a+b+c)(ab+bc+ca)}{abc}=x$ where a, b, c are distinct real numbers, then x is always greater than

1. 30
2. 15
3. 17
4. 9

Q.

To reach playground Ramu has to travel 4 km from his home. Ramu travelled 2 km by bus with a speed of 40 km/hr and remaining 2 km by bicycle with speed of 8 km/hr. Find the average speed.

1. 13.33

2. 15

3. 10

4. 16.33

Q. Question 3 (iv)
In the following APs, find the missing term in the boxes.

Q. If a, b, c are in A.P. then b is known as arithmetic mean and it is given by $b=\frac{a+c}{2}$

1. False
2. True

Q.

If ⁿP₄ = 12 ⁿP₂ the find n.

Q. If a² , b², c² are in AP, prove that a/b+c , b/c+a , c/a+b are in AP

Q.

If numbers n -2, 4n -1 and 5n +2 are in A.P., find the value of n and its next two terms.

Q. In an A.P. of 50 terms the sum of first 10 terms is 210 and the sum of last 15 terms is 2565. Find the A.P.

Q.

If 5x - 3 ≤ 5 + 3x ≤ 4x + 2, solve for x and represent it on the number line x ∈ R

1. 

2. 

3. 

4. 

Q. Q. 3|x| + 5|y|=8 , 7|x| - 3 |y| =48 , then find the value of x+y .

Q.

Determine the value of k for which $k^2+4k+8,2k^2+3k+6$ and $3K^2+4k+4$ are in A.P.

Q.

If the $(m+1)\mathrm{th},(n+1)\mathrm{th}\mathrm{and}(r+1)\mathrm{th}$ terms of an A.P. are G.P. and $\mathrm{m},\mathrm{n},\mathrm{r}$ are in H.P., then the value of the ratio of the common difference to the first term of the A.P. will be: