Word problems based on APs

Correct answer: B. (1440)

The tile numbers are (12,20,28,\ldots) and (S_{18}=1440). Exam tip: find the total of a pattern using the sum formula.

Correct answer: C. (2400)

The sales form the AP (150,170,190,\ldots) and (S_{10}=2400). Exam tip: treat daily sales as AP terms.

Correct answer: B. (60)

Using (S_{15}=8550) and (a=150) gives (d=60). Exam tip: find the common difference from total and first term.

Correct answer: C. 17

The amount filled each minute forms an arithmetic progression with first term 30 and common difference 11. Thus, the amount in the nth minute is 30 + (n-1)×11. For 206 litres, 30 + (n-1)×11 = 206, so (n-1)×11 = 176 and n = 17. Therefore, 206 litres are filled in the 17th minute. In the 16th minute, the amount is 195 litres, so it is a close but incorrect option. Exam tip: use a_n = a+(n-1)d when a particular term of an AP is given.

Correct answer: D. (1944)

The patient numbers are (40,48,56,\ldots) and (S_{18}=1944). Exam tip: use the sum formula for total patients.

Correct answer: B. (1210)

The sack numbers are (60,70,80,\ldots) and (S_{11}=1210). Exam tip: treat each row as one term of the AP.

Correct answer: C. (1331)

The video numbers are (8,13,18,\ldots) and (S_{22}=1331). Exam tip: take the number of weeks as the number of terms.

Correct answer: A. (855)

The lane numbers are (9,13,17,\ldots) and (S_{19}=855). Exam tip: treat a sequence with equal increase as an AP.

Correct answer: C. (128)

The number of drawings is (16,24,32,\ldots) and (a_{15}=128). Exam tip: work done on the (n)th day is the (n)th term.

Correct answer: D. (901)

The marks form the AP (5,11,17,\ldots) and (S_{17}=901). Exam tip: take the number of questions as (n) and find the sum.

Correct answer: A. (900)

The correct answer is A. The numbers of lights are an arithmetic progression with first term \\(a=60\\), common difference \\(d=15\\), and \\(n=8\\) gates. Apply \\(S_n=\frac{n}{2}[2a+(n-1)d]\\): \\(S_8=\frac{8}{2}[2(60)+7(15)] =4(120+105)=4\times225=900\\). Therefore option A is correct. The actual terms are 60, 75, 90, 105, 120, 135, 150 and 165; their total is 900. Option B, 930, is too large and may result from adding one extra increase. Option C, 960, is still larger and does not represent the eight terms. Option D, 990, is larger again and may come from treating the number of gaps incorrectly. Remember that eight gates mean eight terms and seven increases after the first gate. Memory cue: for n objects, the last term uses \\(n-1\\) increases.

Correct answer: B. (12)

The instrument numbers are (25,35,45,\ldots) and (S_n=960) gives (n=12). Exam tip: when a total target is given, find the number of terms.

Correct answer: C. (1040)

The distances form the AP (20,26,32,\ldots) and (S_{16}=1040). Exam tip: treat each hour's distance as a term.

Correct answer: D. (2555)

The weekly sales are (85,100,115,\ldots) and (S_{14}=2555). Exam tip: use the sum formula to add sales across weeks.

Correct answer: A. (1440)

The page numbers are (30,38,46,\ldots) and (S_{16}=1440). Exam tip: use the sum formula for total printing.

Correct answer: B. (1800)

The cloth sales form (100,125,150,\ldots) and (S_9=1800). Exam tip: use the sum formula for sales across all days.

Correct answer: D. (2070)

The member numbers are (18,27,36,\ldots) and (S_{20}=2070). Exam tip: add all days for total members.

Correct answer: C. (6)

Using (S_{16}=1120) and (a=25) gives (d=6). Exam tip: find the common difference from total and first term.

Correct answer: B. (930)

The plate numbers are (20,26,32,\ldots) and (S_{15}=930). Exam tip: treat each table as one term of the AP.

Correct answer: C. (792)

The doses form the AP (10,14,18,\ldots) and (S_{18}=792). Exam tip: add the terms for the total dose.

Correct answer: D. (2550)

The water amounts are (120,150,180,\ldots) and (S_{10}=2550). Exam tip: treat hourly filled water as AP terms.

Correct answer: B. 15

This is an arithmetic progression with first term 110 and common difference 15. The sales on the nth day are \(a_n=110+(n-1)\times15\). Putting \(a_n=320\), we get \(110+15(n-1)=320\), so \(15(n-1)=210\), \(n-1=14\), and \(n=15\). Therefore, 320 newspapers will be sold on the 15th day. The nearby option 13 is incorrect because sales on that day would be \(110+12\times15=290\). Exam tip: In day-number AP questions, remember to use \(n-1\).