Word problems based on APs

The production is the decreasing AP (120,112,104,\ldots) and (S_{11}=880). Exam tip: treat a decrease as a negative common difference.

Using (S_{12}=990) and (d=6) gives (a=50). Exam tip: solve the sum formula for the unknown first term.

From (20+(n-1)8=116), (n=13). Exam tip: set (a_n) equal to the given number to find the required day.

The seats are (19,24,29,\ldots) and (S_{14}=714). 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_{15}=780+14(-35)=290). Exam tip: write the decrease as a negative difference.

The monthly deposits form an arithmetic progression. The first deposit is a = ₹2,000, the number of months is n = 8, and the total is S_8 = ₹26,000. Apply the sum formula S_n = n/2 [2a + (n - 1)d]. Thus, 26,000 = 8/2 [2(2,000) + 7d] = 4(4,000 + 7d). Dividing by 4 gives 6,500 = 4,000 + 7d, so 7d = 2,500 and d = ₹2,500/7, which is not ₹350 exactly. Therefore the supplied numerical data are internally inconsistent with option B. If the intended total were ₹26,450, then d would be ₹350. This item requires revision rather than a passing decision.

The distances are (15,19,23,\ldots) and (S_{12}=444). Exam tip: the number of gaps and the number of poles are different.

The salary forms an AP and (a_{10}=22000+9(600)=27400). Exam tip: find the monthly salary using the (n)th term.

The marks form the AP (4,7,10,\ldots) and (S_{15}=375). Exam tip: take the number of questions as (n) and find the sum.

The participant numbers are (24,31,38,\ldots) and (S_9=468). Exam tip: treat each round as one term.

The harvest is the AP (6,8,10,\ldots) and (S_{12}=204). Exam tip: use the sum formula for total area.

The amounts are (30,60,90,\ldots) and (S_n=1980) gives (n=11). Exam tip: when a total target is given, find the number of terms.

The bulb numbers are (72,66,60,\ldots) and (a_{10}=18). Exam tip: keep the difference negative when moving upward.

The fares are (75,87,99,\ldots) and (S_{10}=1290). Exam tip: treat the fare for each kilometre as one term.

The seats are (13,17,21,\ldots) and (S_{18}=846). Exam tip: use the usual sum formula for odd or even rows.

Using (S_6=30000) and (a=3000) gives (d=800). Exam tip: equal increase in instalments is the common difference.

The lane numbers are (4,7,10,\ldots) and (S_{13}=286). Exam tip: treat a sequence with equal increase as an AP.

The profits are (30000,33000,36000,\ldots) and (S_7=273000). Exam tip: view yearly profits as AP terms.

Putting (S_n=770) gives (n=14). Exam tip: when a total target is given, find the number of terms.

The tile numbers are (10,17,24,\ldots) and (a_{11}=80). Exam tip: take the figure number as the term number.