Word problems based on APs

Using (S_7=588) and (a=60) gives (d=8). Exam tip: daily increase can be found from total distance.

The packet numbers are (30,35,40,\ldots) and (S_{12}=690). Exam tip: take the number of rows as the number of terms.

The sales form the decreasing AP (90,84,78,\ldots) and (S_{10}=630). Exam tip: take (d) negative for decreasing sales.

The work hours are (10,12,14,\ldots) and (S_{12}=252). Exam tip: add all days using the sum formula for total hours.

The member numbers are (30,36,42,\ldots) and (S_{10}=570). Exam tip: treat monthly new members as AP terms.

The matchstick numbers are (8,13,18,\ldots) and (a_{14}=73). Exam tip: in pattern questions check whether the difference is constant.

The page numbers are (25,43,61,\ldots) and (a_9=169). Exam tip: find the (n)th term for a particular month.

The light numbers are (36,42,48,\ldots) and (S_{10}=630). Exam tip: treat each gate as one term.

Using (S_{10}=3250) and (d=30) gives (a=190). Exam tip: the first term can be found from total sum and difference.

The patient numbers are (42,48,54,\ldots) and (S_9=594). Exam tip: use the sum formula for total patients.

The passenger numbers are (18,22,26,\ldots) and (a_{13}=66). Exam tip: take the stop number as the term number.

Using (S_{15}=990) and (a=24) gives (d=6). Exam tip: find the common difference from the total and first term.

The box numbers are (28,35,42,\ldots) and (S_9=504). Exam tip: total can also be found using the average of first and last shelves.

The user numbers are (180,210,240,\ldots) and (a_{12}=510). Exam tip: find a particular day's value using the (n)th term.

Using (S_{10}=670) and (a=22) gives (d=10). Exam tip: find the increase from total members and the first month.

The capacity forms the AP (20,25,30,\ldots) and (S_{12}=570). Exam tip: use the sum formula for total capacity of rows.

This is an arithmetic progression with first term \(a=12\) and common difference \(d=4\). The number of videos in the \(n\)th week is \(a_n=12+(n-1)\times4\). Solving \(12+(n-1)\times4=60\) gives \(n-1=12\), so \(n=13\). Therefore, 60 videos will be uploaded in the 13th week. The close distractor 12 is incorrect because the 12th week has only \(56\) videos. Exam tip: in AP word problems, identify \(a\), \(d\), and the required \(a_n\) before forming the equation.

The pot sales are (24,30,36,\ldots) and (S_{11}=594). Exam tip: use the sum formula to add sales across all days.

The distances form the AP (80,88,96,\ldots) and (S_8=864). Exam tip: treat the distance of each hour as a separate term.

The number of drawings is (8,13,18,\ldots) and (a_{13}=68). Exam tip: work done on the (n)th day is the (n)th term.