Arithmetic Mean (AM)

When three quantities are in A.P., then the middle one is called as arithmetic mean of other two. If ‘a’ and ‘b’ are two numbers and A be the arithmetic mean of a and b, then a, A, b are in A.P.

question 1. If is the A.M. between p and q. Then, find the value of a

Solution: We have,

A.M. between p and q  = p + q/2

It is given that

is the A.M. between p and q.

∴ = p + q/2

question 1. If 2x, x + 10, 3x + 2 are in A.P., find the value of x.

Solution: Since, 2x, x + 10, 3x + 2are in A.P.

∴ 2(x + 10) = 2x + (3x + 2)

⇒ 2x + 20 = 5x + 2

⇒ 3x = 18

⇒ x = 6

question 2. If the numbers a, b, c, d, e form an A.P., then find the value of a – 4b + 6c – 4d + e.

Solution: Let D be the common difference of the given A.P. Then,