Question

A stadium staircase with 150 steps is numbered from 1 to 150. Jan starts on step 130 and steps down to step number 127, then to step number 124, and continues downward to step 13 stepping only on every third step. Jen starts on step number 3 and steps up to step number 7, then to step number 11, and continues upward to step 139 stepping only on every fourth step. How many steps were stepped on by both Jan and Jen (not necessarily at the same time)?

Answer 1

• Therefore, the number of steps Jan made is 40.

• Therefore, the number of steps Jen made is 35.

Explanation:

Jan Starts on Step 130 and steps down to step number 127, then to step number 124, and continues downward to step 13 stepping only on every third step.

Jan's Movement can be represented by the sequence:

130, 127, 124,...13

The goal is to find the number of terms in the given sequence.

The following can be derived form the arithmetic sequence

First term =130

Common Difference = -3

Last Term =13

`Last \: Term = a+(n-1)d\\13=130+(n-1)(-3)\\-117=-3n+3\\-117-3=-3n\\-120=-3n\\n=40`

• Therefore, the number of steps Jan made is 40.

Jen starts on step number 3 and steps up to step number 7, then to step number 11, and continues upward to step 139 stepping only on every fourth step.

Jen's Movement can be represented by the sequence:

3,7,11,...139

The goal is to find the number of terms in the given sequence.

The following can be derived form the arithmetic sequence

First term =3

Common Difference = 4

Last Term =139

`Last \: Term = a+(n-1)d\\139=3+(n-1)(4)\\139-3=4n-4\\139-3+4=4n\\140=4n\\n=35`

• Therefore, the number of steps Jen made is 35.