Question

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

Answer 1

Answer:

The middle term in the sequence is 12.

Arithmetic mean of the sequence is x  = 12

Step-by-step 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  = $\frac{\textrm{Sum of observations}}{\textrm{Number of observations}}$

⇒ $\frac{8+ 12+ 16}{3}   = \frac{36}{3} = 12$

Arithmetic Mean  = 12