Question

You have a job as a teacher. Your salary for the first year is $37,185.

You will receive a 6% increase every year.
Part A Would an arithmetic or geometric sequence best model this situation?
- Arithmetic
- Both
- Neither
- Geometric

Part B: What explicit formula models this situation?
- an=37185*(.06)^n-1
- an=37185*(1.06)^n-1
- an=6*(37185)^n-1
- an=6*(1.06)^n-1

Part C: How much will your salary be at the start of your 5th year?
- $37,192.57
- $42,564.25
- $46,945.21
- $223,110.00

Answer 1

a). Geometric sequence

b).

c). $46945.21 will be the salary at the start of 5th year.

Explanation:

My salary for the first year is $37185.

If I get an increase of 6% every year then the next year salary will be,

= $39416.1

Similarly in the second year my salary will be

= $41781.07

So the sequence becomes $37185, $39416.1 $41781.07.....

And there is a common ratio in each successive term 'r' = 1.06

a). Therefore, it's a geometric sequence.

b). Explicit formula for this sequence will be in the form of

Where t = duration in years

c). Salary at the start of 5th year,

= $46945.21

Explanation: