Question

2, x, 14 are in Arithmetic progression, then the value of x is
A. 28
B. 16
C. 7
D. 8​

Answer 1

Answer:

a=2

3rd term is 14..so

a+2d=14

2+2d=14

2d=12

d=12/2=6

so, x is second term

so,

a+d=x

x=2+6=8

x=8 answer

Step-by-step explanation:

Answer 2

Answer:

Required value of x is 8.

Option D is the correct answer.

Step-by-step explanation:

Given series is 2,x,14.

This is a Arithmetic progression.

So we can say common difference of these numbers are same.

Common difference between 2 an x is $x - 2$

and common difference between x and 14 is $14 - x$

So,$x - 2 = 14 - x$

We are separating variable part and constant part,

$x + x = 14 + 2$

$2x = 16$

$x = \frac{16}{2}$

$x = 8$

Therefore value of x is 8.

Another method,

First term of the given series is 2 and common difference is (x-2)

Here 14 is the 3 rd term of the series.

We know nth term is AP series,$a_n = a+(n-1)d$

According to question,

$14 = 2 + (3 - 1)(x - 2)$

$2 + 2(x - 2) = 14$

$2 + 2x - 4 = 14$

$2x = 14 + 4 - 2 = 16$

$x = \frac{16}{2} = 8$