Word problems based on APs

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 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.

The member numbers are (36,48,60,\ldots) and (S_{19}=2736). Exam tip: add all days for total members.

Using (S_{21}=2793) and (a=42) gives (d=9). Exam tip: find the common difference from total and first term.

The plate numbers are (30,40,50,\ldots) and (S_{18}=2070). Exam tip: treat each table as one term of the AP.

The doses form the AP (15,21,27,\ldots) and (S_{22}=1716). Exam tip: add the terms for the total dose.

The water amounts are (200,245,290,\ldots) and (S_{12}=5370). Exam tip: treat hourly filled water as AP terms.

This is an AP with first term \(a=160\) and common difference \(d=30\). Sales on the \(n\)th day are \(a_n=160+(n-1)30\). Setting this equal to 610 gives \(160+(n-1)30=610\), so \((n-1)30=450\), \(n-1=15\), and \(n=16\). Therefore, 610 newspapers will be sold on the 16th day. On the 15th day, the sales would be 580, so that close option is incorrect. Exam tip: for a target value in an AP, equate it to \(a_n=a+(n-1)d\).