1Define arithmetic mean.
2What does 'n' represent in the formula \( d = \frac{b-a}{n+1} \)?
3Write the meaning of 'b' in the formula \( d = \frac{b-a}{n+1} \).
4State an arithmetic mean between -20 and 20.
5Find the arithmetic mean between (a + b) and (a - b).
6If the arithmetic mean between x and 2x is 3, find the value of x.
7If the arithmetic mean between y - 1 and 2y is 7, find the value of y.
8In an AP, the 4th mean is 12 and the ratio of the first mean to the 4th mean is 2/3. Find the first mean.
9Write the number of the term which is equal to the 5th mean.
10In an AP, the 10th and 12th terms are 100 and 120. Find the 11th term.
11If 10, x, 20 are in AP, find x.
12Find the values of x and y if 10, x, y, 25 are in AP.
13If -13, p, q, r, 7 are in AP, find the values of p, q and r.
14If l, m and n are in AP, show that \( m = \frac{l+n}{2} \).
15If the arithmetic mean between two numbers is 50 and the second number is 60, find the first number.
16Two numbers are in the ratio 2 : 3. If their AM is 20, find the numbers.
17Insert two arithmetic means between 4 and 22.
18Insert two arithmetic means between 100 and 10.
19Insert 5 arithmetic means between 10 and 70.
20Insert 6 arithmetic means between 11 and 39.
21There are 'n' arithmetic means between 15 and 45. If the third mean is 30, find the value of n. Also find the ratio of the 3rd mean to the 5th mean.
22Some arithmetic means are inserted between 9 and 33. If the third mean is 21, find the number of means and the values of the remaining means.
23If 'n' arithmetic means are inserted between 5 and 35 and the ratio of the second mean to the last mean is 1 : 4, find the value of n.
24There are 6 AMs between a and b. If the 2nd mean and the 5th mean are 11 and 23, find the values of a and b.
25How many terms does an AP have if 8 arithmetic means are inserted between two numbers?
26Insert 4 arithmetic means between 3 and -12.
27Is 3 the arithmetic mean of 1 and 6? Give a reason.