Question

2, 6, 10, 14, ...

In the sequence above, each term after the first is 4 greater than the preceding term. Which of the following is not a term in the sequence?

A. 90
B. 150
C. 160
D. 170
E. 210

Answer 1

The sequence can be represented by
`2 + 4x`, where
`x` is a whole number(
`x \geq 0` and
`x` is an integer). By this, we should be able to plug in some whole number x and be able to get these values if they are in the sequence. To test this, let's set these numbers equal to
`2 + 4x` and confirm that there is a whole number x which equals the values selected.

`2 + 4x = 90 \Rightarrow 4x = 88 \Rightarrow x = 22 \, \checkmark`

`2 + 4x = 150 \Rightarrow 4x = 148 \Rightarrow x = 37 \, \checkmark`

`2 + 4x = 160 \Rightarrow 4x = 158 \Rightarrow x = 39.5`

When trying 160 with our equation, we find that x doesn't equal a whole number, thus our answer is C, or 160. To confirm our answer, we can test 170 and 210 and confirm that they both give us a value for x which is a whole number.

`2 + 4x = 170 \Rightarrow 4x = 168 \Rightarrow x = 42 \, \checkmark`

`2 + 4x = 210 \Rightarrow 4x = 208 \Rightarrow x = 52 \, \checkmark`