Word problems based on APs

Correct answer: C. (1896)

The video numbers are (10,16,22,\ldots) and (S_{24}=1896). Exam tip: take the number of weeks as the number of terms.

Correct answer: C. (1302)

The lane numbers are (12,17,22,\ldots) and (S_{21}=1302). Exam tip: treat a sequence with equal increase as an AP.

Correct answer: C. (229)

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.

Correct answer: C. (936)

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.

Correct answer: C. (1440)

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

Correct answer: C. (14)

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.

Correct answer: C. (1845)

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

Correct answer: C. (3146)

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

Correct answer: C. (14400)

The direct answer is C, 14400 rupees. Daily income forms an arithmetic progression: 900, 1075, 1250, and so on. The first term is \(a=900\), the common difference is \(d=175\), and there are \(n=9\) days. Apply \(S_n=\frac{n}{2}[2a+(n-1)d]\). Thus \(S_9=\frac{9}{2}[2(900)+8(175)]\). Calculate step by step: \(2(900)=1800\), \(8(175)=1400\), and the bracket is \(3200\). Therefore \(S_9=\frac{9}{2}\times3200=9\times1600=14400\). Option A, 13800, is too small and may come from an incorrect difference or incomplete addition. Option B, 14100, does not match the AP sum. Option C, 14400, is exactly the calculated total and is correct. Option D, 14700, is too large and may result from counting an extra day or increase. The question asks total income, so we must add all nine daily incomes, not calculate only the ninth day. Exam cue: “total for 9 days” means use the sum formula, while “income on the ninth day” would require only the nth-term formula.

Correct answer: C. (1989)

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

Correct answer: C. (2750)

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

Correct answer: C. (2904)

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

Correct answer: C. (7)

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

Correct answer: C. (1344)

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

Correct answer: C. (1190)

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

Correct answer: C. (2790)

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

Correct answer: C. 16

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 \(a_n=a+(n-1)d\).

Correct answer: C. (25)

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.

Correct answer: B. (627600)

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

Correct answer: D. (8640)

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

Correct answer: C. (5)

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

Correct answer: C. 22

The numbers of plants form an arithmetic progression with first term \(a=21\) and common difference \(d=11\). The number of plants in the \(n\)th row is \(a_n=21+(n-1)\times 11\). Setting this equal to 252 gives \(21+(n-1)\times 11=252\), so \(11(n-1)=231\), \(n-1=21\), and \(n=22\). Hence, the 22nd row has 252 plants. The 21st row would have only 241 plants. Exam tip: when a target term is given, equate it to \(a_n\) and solve for \(n\).

Correct answer: B. (3060)

The daily work forms the AP (68,82,96,\ldots) and (S_{17}=3060). Exam tip: treat the daily increase as the common difference.

Correct answer: B. (12)

The amounts are (350,500,650,\ldots) and (S_n=12600) gives (n=12). Exam tip: set the target total equal to (S_n).

Correct answer: C. 15

The numbers of stones form a decreasing AP from the bottom, with \(a=210\) and \(d=-10\). For the \(n\)th row, \(a_n=210+(n-1)(-10)\). Using \(210-10(n-1)=70\) gives \(n-1=14\), so \(n=15\). Hence, the 15th row has 70 stones. The 14th row would have 80 stones, so it is not correct. Exam tip: use a negative common difference for an AP that decreases upward.