Question

Given the third term is 12 and the rate of change is 3. What is the 5th term

Answer 1

Answer:

The 5th term:

a₅ = 18

Step-by-step explanation:

We know that Arithmetic sequences have a constant rate of change.

Given

• a₃ = 12

• common difference = rate pf change = d = 3

The nth term of the Arithmetic sequence with a₁ and 'd' is defined as

aₙ = a₁ + (n-1)d

Where

a₁ is the first term

d is the common difference

as

a₃ = 12

d = 3

so

Plug in n=3

a₃ = a₁ + (3-1)d

Now Plug in a₃ = 12 and d = 3

12 = a₁ + (3-1)3

12 = a₁ + 2(3)

12 = a₁ + 6

a₁ = 6

so

Formula to find the 5th term

a₅ = a₁ + 4d

Plug in a₁ = 6 and d = 3

a₅ = 6 + 4(3)

a₅ = 18

Therefore, the 5th term:

a₅ = 18