Answer:
It seems like there is a pattern in Lincoln's earnings each week. Let's first identify the pattern by looking at the increase in earnings from week to week:
Week 1 to Week 2: $180 - $120 = $60 increase
Week 2 to Week 3: $240 - $180 = $60 increase
Week 3 to Week 4: $300 - $240 = $60 increase
From this, we can see that Lincoln's earnings are increasing by $60 each week. This is a linear pattern, and we can use it to predict future earnings.
To find the total earnings for week 6, we can continue the pattern:
Week 4 to Week 5: $300 + $60 = $360
Week 5 to Week 6: $360 + $60 = $420
So, Lincoln's total earnings for week 6 would be $420.
To confirm this, we can also use the formula for the nth term of an arithmetic sequence, which is given by:
a_n = a_1 + (n - 1)d
where:
a_n is the nth term (week 6 earnings in this case)
a_1 is the first term (week 1 earnings)
n is the term number (6 for week 6)
d is the common difference between the terms (the weekly increase of $60)
Let's plug in the values:
a_6 = $120 + (6 - 1) * $60
a_6 = $120 + 5 * $60
a_6 = $120 + $300
a_6 = $420
So, Lincoln's total earnings at week 6 would indeed be $420.
Step-by-step explanation: