Word problems based on APs

The number of drawings is (25,37,49,\ldots) and (a_{18}=229). Exam tip: work done on the (n)th day is the (n)th term.

The marks form the AP (6,13,20,\ldots) and (S_{16}=936). Exam tip: take the number of questions as (n) and find the sum.

The light numbers are (80,100,120,\ldots) and (S_9=1440). Exam tip: treat each gate as one term.

The instrument numbers are (30,42,54,\ldots) and (S_n=1512) gives (n=14). Exam tip: when a total target is given, find the number of terms.

The distances form the AP (26,35,44,\ldots) and (S_{18}=1845). Exam tip: treat each hour's distance as a term.

The weekly sales are (110,132,154,\ldots) and (S_{13}=3146). Exam tip: use the sum formula to add sales across weeks.

The income is (900,1075,1250,\ldots) and (S_9=14400). Exam tip: add daily income as AP terms.

The numbers of windows form an arithmetic progression with first term a = 220 and common difference d = −20, because the number decreases by 20 on each successive floor. The nth-term formula is aₙ = a + (n − 1)d. Substituting the required number 40 gives 40 = 220 + (n − 1)(−20). Hence, −180 = −20(n − 1), so n − 1 = 9 and n = 10. Therefore, the tenth floor has 40 windows, making option C correct. Checking the sequence confirms this: floor 1 has 220 windows, floor 2 has 200, and after nine decreases of 20, floor 10 has 40. The other choices correspond to 60, 80 or 20 windows.

The page numbers are (45,54,63,\ldots) and (S_{17}=1989). Exam tip: use the sum formula for total printing.

The cloth sales form (140,170,200,\ldots) and (S_{10}=2750). Exam tip: use the sum formula for sales across all days.

The member numbers are (27,37,47,\ldots) and (S_{22}=2904). Exam tip: add all days for total members.

Using (S_{19}=1805) and (a=32) gives (d=7). Exam tip: find the common difference from total and first term.

The plate numbers are (24,32,40,\ldots) and (S_{16}=1344). Exam tip: treat each table as one term of the AP.

The doses form the AP (12,17,22,\ldots) and (S_{20}=1190). Exam tip: add the terms for the total dose.

The water amounts are (150,190,230,\ldots) and (S_9=2790). Exam tip: treat hourly filled water as AP terms.

This is an arithmetic progression with first term \(a=140\) and common difference \(d=25\). Sales on the \(n\)th day are \(a_n=140+(n-1)25\). Setting this equal to 515 gives \(140+(n-1)25=515\), so \((n-1)25=375\), \(n-1=15\), and \(n=16\). Option 15 results from incorrectly treating \(n-1\) as the day number. Exam tip: for day-based AP questions, use \(a_n=a+(n-1)d\).

The seats form an AP and (S_n=2840) gives (n=25). Exam tip: when total seats are given, find (n) using the sum formula.

The salaries form the AP (38000,40600,43200,\ldots) and (S_{12}=627600). Exam tip: use (S_n) to add all months.

The production is the decreasing AP (720,696,672,\ldots) and (S_{16}=8640). Exam tip: treat decrease as a negative common difference.

Using (S_{22}=1782) and (a=30) gives (d=5). Exam tip: find the common difference from total and first term.