If 3, x, y, 18 are in arithmetric progression, find the value of x and y

Given:

arithmetic progression

a₁ = 3

a₂ = x

a₃ = y

a₄ = 18

Solution:

The arithmetic progression has general formula to determine nth term

a₁ + d (n - 1) = an

a₁ represents first term, d represents difference, n represents number of terms, an represents nth term

First we should find out the value of d, by submitting a₄ to the formula

a₁ + d (n - 1) = an

a₁ + d (4 - 1) = a₄

3 + d (3) = 18

3 + 3d = 18

3d = 15

d = 5

The difference of the sequence is 5

Second, determine x and y

x = a₂

x = a₁ + d (2 - 1)

x = 3 + 5 (1)

x = 8

y = a₃

y = a₁ + d (3 - 1)

y = 3 + 5 (2)

y = 13

The value of x is 8, the value of y is 13