Answer:
The sequence is:
5, 14, 23, 32
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