Algebra Word Problem

Question

Travis will be paid $1 week for the first week he works, $5 for the second week, $25 for the third week, $125 for the fourth week. Write an expression that represents what he would be paid in the 30th week

Answer 1

The above is the correct answer. An intuitive way to understand this is that pay increases by a multiple of $5 each week after the first.

Week 1 pay = $1

Week 2 pay = week 1 pay × $5 = $5 or $5^1

Week 3 pay = week 2 pay × $5 = $25 or $5^2

...

Week 30 pay = week 29 pay × $5 = $5^(30-1) or $5^29

Answer 2

1, 5, 25, 125, ... is a geometric sequence with common ratio r = 5.

a_n, the nth term, can be expressed as a_n = a₁r^n-1

So, for this particular example, we have a₃₀ = (1)(5)^30-1 = 5²⁹.