The 2nd 3rd and 4th term of an aritmetic progression

are x-2, 5 and x+2 respectively. Find x

2 answers

We can use the formula for the nth term of an arithmetic progression:

a_n = a_1 + (n-1)d

Where a_1 is the first term, d is the common difference, and n is the term number.

Using the given information:

a_2 = x-2
a_3 = 5
a_4 = x+2

We can find the common difference, d, by subtracting a_2 from a_3, or by subtracting a_3 from a_4:

d = a_3 - a_2 = 5 - (x-2) = 7-x

d = a_4 - a_3 = (x+2) - 5 = x-3

Setting these expressions equal to each other:

7-x = x-3

Solving for x:

2x = 10

x = 5

Therefore, the value of x is 5.
To make a long story short:

To be in an AS,
5 - (x-2) = x+2 - 5
5 - x + 2 = x + 2 - 5
-2x = -10
x = 5