Word problems based on APs

The passenger numbers are (8,13,18,\ldots) and (S_{19}=1007). Exam tip: take the number of stops as the number of terms.

The profits form the AP (60000,68000,76000,\ldots) and (S_6=480000). Exam tip: treat yearly profits as separate terms.

The tile numbers are (9,16,23,\ldots) and (S_{15}=870). Exam tip: find the total of a pattern using the sum formula.

The sales form the AP (120,135,150,\ldots) and (S_9=1620). Exam tip: treat daily sales as AP terms.

Using (S_{12}=4500) and (a=100) gives (d=50). Exam tip: find the common difference from total and first term.

The amount filled per minute forms an arithmetic progression with first term 20 and common difference 9. Therefore, the amount filled in the nth minute is \(a_n=20+(n-1)\times 9\). Using \(20+(n-1)\times 9=137\), we get \((n-1)\times 9=117\), so \(n-1=13\) and \(n=14\). Hence, 137 litres are filled in the 14th minute. In the 13th minute, the amount would be only 128 litres. Exam tip: equate the target amount to the nth term \(a_n\) of the AP and solve for n.

The patient numbers are (35,40,45,\ldots) and (S_{20}=1650). Exam tip: use the sum formula for total patients.

The sack numbers are (45,53,61,\ldots) and (S_{10}=810). Exam tip: treat each row as one term of the AP.

The video numbers are (5,9,13,\ldots) and (S_{20}=860). Exam tip: take the number of weeks as the number of terms.

The lane numbers are (6,9,12,\ldots) and (S_{16}=456). Exam tip: treat a sequence with equal increase as an AP.

The number of drawings is (14,20,26,\ldots) and (a_{12}=80). Exam tip: work done on the (n)th day is the (n)th term.

The marks form the AP (3,7,11,\ldots) and (S_{18}=666). Exam tip: take the number of questions as (n) and find the sum.

The light numbers are (48,60,72,\ldots) and (S_9=864). Exam tip: treat each gate as one term.

The instrument numbers are (20,25,30,\ldots) and (S_n=570) gives (n=12). Exam tip: when a total target is given, find the number of terms.

The distances form the AP (18,22,26,\ldots) and (S_{15}=690). Exam tip: treat each hour's distance as a term.

The weekly sales are (70,80,90,\ldots) and (S_{12}=1500). Exam tip: use the sum formula to add sales across weeks.

The income is (500,600,700,\ldots) and (S_{10}=9500). Exam tip: add daily income as AP terms.

This is an arithmetic-progression word problem involving the nth term. The first floor has a = 150 windows and each succeeding floor has 10 fewer, so the common difference is d = −10. For the nth floor, aₙ = a + (n−1)d. Substituting the required number gives 60 = 150 + (n−1)(−10). Hence −90 = −10(n−1), so n−1 = 9 and n = 10. Therefore option C is correct. The sequence is 150, 140, 130, ..., 60, and 60 is the tenth term. The other choices correspond to different window counts.

The page numbers are (25,32,39,\ldots) and (S_{13}=871). Exam tip: use the sum formula for total printing.

The cloth sales form (80,100,120,\ldots) and (S_8=1200). Exam tip: use the sum formula for sales across all days.