Word problems based on APs

The seats are (7,9,11,\ldots) and (S_{21}=567). Exam tip: use the usual sum formula even for an odd number of rows.

Putting (S_n=450) gives (n=12). Exam tip: when a total target is given, find the number of terms.

The deposits are (60,75,90,\ldots) and (a_{10}=195). Exam tip: use (a_n) for the amount on a particular day.

The box numbers are (25,30,35,\ldots) and (S_{11}=550). Exam tip: total can also be found using the average of first and last shelves.

Using (S_{15}=3150) and (d=10) gives (a=140). Exam tip: the first term can be found from total sum and difference.

The seats are (13,16,19,\ldots) and (S_{14}=455). Exam tip: convert real-life seating questions into APs.

The savings form the AP (120,150,180,\ldots) and (S_{10}=2550). Exam tip: use the sum formula for total amount.

The seats form an AP and (a_{18}=22+17(4)=90). Exam tip: treat the row number as the term number.

The production is the AP (180,200,220,\ldots) and (S_8=2000). Exam tip: treat the daily increase as the common difference.

Putting (S_n=360) gives (n=15). Exam tip: when total sum is given, form an equation for (n).

The production is the decreasing AP (95,90,85,\ldots) and (S_9=675). Exam tip: treat a decrease as a negative common difference.

Using (S_{10}=725) and (d=5) gives (a=50). Exam tip: solve the sum formula for the unknown first term.

From (18+(n-1)7=88), (n=11). Exam tip: set (a_n) equal to the given number to find the required day.

The seats are (17,20,23,\ldots) and (S_{16}=632). Exam tip: you may also find the last row and use (S_n=\frac{n}{2}(a+l)).

This is a decreasing AP and (a_{13}=640+12(-30)=280). Exam tip: write the decrease as a negative difference.

The governing concept is the sum of the first n terms of an arithmetic progression. The monthly deposits form an AP with first term a = 1,500, number of terms n = 7, total S7 = 16,800, and common difference d equal to the monthly increase. Use S_n = n/2[2a + (n − 1)d]. Substitution gives 16,800 = 7/2[3,000 + 6d]. Multiplying by 2 and dividing by 7 gives 4,800 = 3,000 + 6d, so 6d = 1,800 and d = 300. Hence option B is correct. The other choices result from an incorrect sum or an incorrect division; the required quantity is the common difference, not the final deposit.

The distances are (12,15,18,\ldots) and (S_{10}=255). Exam tip: the number of gaps and the number of poles are different.

The salary forms an AP and (a_9=18000+8(750)=24000). Exam tip: find the monthly salary using the (n)th term.

The marks form the AP (5,7,9,\ldots) and (S_{14}=252). Exam tip: take the number of questions as (n) and find the sum.

The participant numbers are (21,27,33,\ldots) and (S_8=336). Exam tip: treat each round as one term.