Find the 16th term when given: 3, 7, 11, 15

Question

Find the 16th term when given: 3, 7, 11, 15

Answer 1

First you need to determine by how much it changes between numbers, which is +4. You could take the last number they give you and keep adding 4 until you get to the 16th term but that would take a long time. It is better to set up an equation which would be 4(x-1)+3.  you need to substitute the number of the term you need in for x

Answer 2

a_{1 = 3}

 

a₂ = 7

 

a₃ = 11

 

we notice that the next number is 4 more than the previous number

 

we can use the formula below:

 

a_{n =} a₁ + (n - 1)d

 

we have a₁ = 3, d = 4

 

since we're calculating a₁₆, we need n to be equal to 16.

 

a₁₆ = 3 + (16 - 1)4

 

a₁₆ = 3 + 4(15) = 63

 

so, a₁₆ = 63