Word problems based on APs

From (12+(n-1)6=72), (n=11). Exam tip: set (a_n) equal to the given number to find the required day.

Putting (S_n=1080) in the sum formula gives (n=16). Exam tip: choose the correct positive integer answer.

The amounts are (25,50,75,\ldots) and (S_n=1375) gives (n=10). Exam tip: treat multiple-based savings as a simple AP.

The charge increases are (7,10,13,\ldots) and (S_8=140). Exam tip: percentage increases can also be used as AP terms.

The tile numbers are (4,10,16,\ldots) and (a_{12}=70). Exam tip: take the figure number as the term number.

Using (S_5=300) and (a=40) gives (d=10). Exam tip: daily increase can be found from total distance.

The member numbers are (20,28,36,\ldots) and (S_6=240). Exam tip: treat monthly new members as AP terms.

The harvest is the AP (3,5,7,\ldots) and (S_9=99). Exam tip: use the sum formula for total area.

The fares are (50,65,80,\ldots) and (S_8=820). Exam tip: treat the fare for each kilometre as one term.

The lane numbers are (2,3,4,\ldots) and (S_{14}=119). Exam tip: a sequence with small constant increase is also an AP.

The profits are (18000,19000,20000,\ldots) and (S_5=100000). Exam tip: view yearly profits as AP terms.

Putting (S_n=306) in the sum formula gives (n=12). Exam tip: you can also check options in the sum formula.

The production is the decreasing AP (100,95,90,\ldots) and (S_{10}=775). Exam tip: for decreasing production rate, (d) is negative.

The page numbers are (20,35,50,\ldots) and (a_7=110). Exam tip: find the (n)th term for a particular month.

The light numbers are (30,35,40,\ldots) and (S_8=380). Exam tip: treat each gate as one term.

Using (S_6=21000) and (a=2000) gives (d=600). Exam tip: equal increase in instalments is the common difference.

The work hours are (8,12,16,\ldots) and (S_{10}=260). Exam tip: add all days using the sum formula for total hours.

The packet numbers are (18,20,22,\ldots) and (S_{12}=348). Exam tip: take the number of rows as the number of terms.

The sales form the decreasing AP (60,50,40,\ldots) and (S_6=210). Exam tip: take (d) negative for decreasing sales.

The numbers form the AP (5,12,19,\ldots) and (a_{15}=103). Exam tip: work done on the (n)th day is the (n)th term.