Question

Let x be the required Arithmetic Mean,then if 8, x, 16 form three successiveterms in the Aritmetic Progression,x is

Answer 1

The middle term in the sequence is 12.

Arithmetic mean of the sequence is x = 12

Explanation:

Here, three consecutive terms in the AP are 8 , x , 16.

Now, if and three a, b , c terms are in an arithmetic progression.

⇒ b -a = Common difference (d) = c - b

Similarly here, 8 , x , 16 are in AP.

⇒ x - 8 = 16 - x = Common difference d

or, x + x = 16 + 8

or, 2 x = 24

⇒ x = 24/2 = 12

or , x = 12

Hence, the middle term in the sequence is 12.

Also, arithmetic mean of 8, 12, 16 =
`\frac{\textrm{Sum of observations}}{\textrm{Number of observations}}`

⇒
`(8+ 12+ 16)/(3)   = (36)/(3) = 12`

Arithmetic Mean = 12