Word problems based on APs

The passenger numbers are (20,29,38,\ldots) and (S_{17}=1564). Exam tip: take the number of stops as the number of terms.

The profits form the AP (100000,115000,130000,\ldots) and (S_9=1440000). Exam tip: treat yearly profits as separate terms.

The tile numbers are (20,32,44,\ldots) and (S_{17}=1972). Exam tip: find the total of a pattern using the sum formula.

The sales form the AP (210,240,270,\ldots) and (S_{12}=4500). Exam tip: treat daily sales as AP terms.

Using (S_{20}=19300) and (a=250) gives (d=75). Exam tip: find the common difference from total and first term.

The amount filled each minute forms an AP with first term \(a=52\) and common difference \(d=16\). Thus, the amount filled in the \(n\)th minute is \(a_n=52+(n-1)16\). Setting this equal to \(308\), \(52+(n-1)16=308\), so \((n-1)16=256\), \(n-1=16\), and \(n=17\). Therefore, 308 litres are filled in the 17th minute. In the 16th minute, the amount is \(292\) litres, so that close option is incorrect. Exam tip: distinguish between the amount filled in a particular minute and the total amount filled up to that minute.

The patient numbers are (70,82,94,\ldots) and (S_{18}=3096). Exam tip: use the sum formula for total patients.

The sack numbers are (84,98,112,\ldots) and (S_{13}=2184). Exam tip: treat each row as one term of the AP.

The video numbers are (15,22,29,\ldots) and (S_{25}=2475). Exam tip: take the number of weeks as the number of terms.

The lane numbers are (18,24,30,\ldots) and (S_{20}=1500). Exam tip: treat a sequence with equal increase as an AP.

The number of drawings is (36,50,64,\ldots) and (a_{16}=246). Exam tip: work done on the (n)th day is the (n)th term.

The marks form the AP (8,17,26,\ldots) and (S_{15}=1065). Exam tip: take the number of questions as (n) and find the sum.

The light numbers are (90,115,140,\ldots) and (S_{10}=2025). Exam tip: treat each gate as one term.

The instrument numbers are (42,56,70,\ldots) and (S_n=2520) gives (n=15). Exam tip: when a total target is given, find the number of terms.

The distances form the AP (34,42,50,\ldots) and (S_{18}=1836). Exam tip: treat each hour's distance as a term.

The weekly sales are (130,155,180,\ldots) and (S_{14}=4095). Exam tip: use the sum formula to add sales across weeks.

The income is (1200,1450,1700,\ldots) and (S_{10}=23250). Exam tip: add daily income as AP terms.

The numbers of windows form an arithmetic progression with first term a = 260 and common difference d = −18, because the number decreases by 18 on every successive floor. For the nth floor, use a_n = a + (n − 1)d. Substituting the given number of windows gives 62 = 260 + (n − 1)(−18). Hence, 62 − 260 = −198, so n − 1 = 11 and n = 12. A quick check confirms the result: the twelfth floor has 260 − 11 × 18 = 260 − 198 = 62 windows. Therefore option C is correct; the other choices result from an incorrect step count or sign.

The page numbers are (60,71,82,\ldots) and (S_{18}=2763). Exam tip: use the sum formula for total printing.

The cloth sales form (160,195,230,\ldots) and (S_{11}=3685). Exam tip: use the sum formula for sales across all days.