Question

Write an Equation using the following arithmetic sequence: 5, _____, ______, 32

Answer 1

Answer:

The sequence is:

5, 14, 23, 32

Step-by-step explanation:

We know that an Arithmetic sequence with a₁ and the commo difference 'd' has the nth term such as:

aₙ = a₁ + (n-1)d

Given the arithmetic sequence

5, _____, ______, 32

here:

a₁ = 5

n = 4

aₙ

so substituting a₁ = 5, n = 4 and aₙ = 32 in the nth term

aₙ = a₁ + (n-1)d

32 = 5 + (4-1)d

32 = 5 + 3d

3d = 32-5

3d = 27

divide both sides by 3

3d/3 = 27/3

d = 9

Therefore, the common difference: d = 9

Determining the 2nd term:

Using the formula

aₙ = a₁ + (n-1)d

substitute n = 2, a₁ = 5, d = 9

a₂ = 5 + (2-1)9

a₂ = 5 + 1(9)

a₂ = 5 + 9

a₂ = 14

Determining the 3rd term:

Using the formula

aₙ = a₁ + (n-1)d

substitute n = 3, a₁ = 5, d = 9

a₃ = 5 + (3-1)9

a₃ = 5 + 2(9)

a₃ = 5 + 18

a₃ = 23

Thus, the sequence becomes:

5, 14, 23, 32