Word problems based on APs

The harvest is the AP (4,7,10,\ldots) and (S_{10}=175). Exam tip: use the sum formula for total area.

The amounts are (40,60,80,\ldots) and (S_n=1120) gives (n=8). Exam tip: when a total target is given, find the number of terms.

The bulb numbers are (60,55,50,\ldots) and (a_9=20). Exam tip: keep the difference negative when moving upward.

The fares are (60,70,80,\ldots) and (S_9=900). Exam tip: treat the fare for each kilometre as one term.

The seats are (11,14,17,\ldots) and (S_{19}=722). Exam tip: use the usual sum formula even for an odd number of rows.

Using (S_5=17500) and (a=2500) gives (d=500). Exam tip: equal increase in instalments is the common difference.

The lane numbers are (5,7,9,\ldots) and (S_{12}=192). Exam tip: a sequence with a small constant increase is also an AP.

The profits are (25000,27000,29000,\ldots) and (S_6=180000). Exam tip: view yearly profits as AP terms.

Putting (S_n=525) gives (n=11). Exam tip: when a total target is given, find the number of terms.

The tile numbers are (7,12,17,\ldots) and (a_{13}=67). Exam tip: take the figure number as the term number.

Using (S_6=405) and (a=45) gives (d=9). Exam tip: daily increase can be found from total distance.

The packet numbers are (24,28,32,\ldots) and (S_{11}=484). Exam tip: take the number of rows as the number of terms.

The sales form the decreasing AP (75,70,65,\ldots) and (S_8=460). Exam tip: take (d) negative for decreasing sales.

The work hours are (12,15,18,\ldots) and (S_9=216). Exam tip: add all days using the sum formula for total hours.

The member numbers are (25,30,35,\ldots) and (S_8=340). Exam tip: treat monthly new members as AP terms.

The matchstick numbers are (9,15,21,\ldots) and (a_{12}=75). Exam tip: in pattern questions check whether the difference is constant.

The page numbers are (30,50,70,\ldots) and (a_8=170). Exam tip: find the (n)th term for a particular month.

The light numbers are (28,35,42,\ldots) and (S_9=504). Exam tip: treat each gate as one term.

Using (S_{12}=3000) and (d=20) gives (a=140). Exam tip: the first term can be found from total sum and difference.

The patient numbers are (36,40,44,\ldots) and (S_{10}=540). Exam tip: use the sum formula for total patients.