Arithmetic Progressions — Questions & Answers

Sample questions from Arithmetic Progressions

1. Q1. In an AP, if a = 3, n = 8 and Sₙ = 192, then the common difference d is:

   • A.6✓
   • B.8
   • C.4
   • D.12
   Solution

   A is correct. From Sₙ = (n/2)[2a + (n − 1)d], 192 = 4[6 + 7d], so 48 = 6 + 7d, giving 7d = 42 and d = 6. B comes from dividing 192 by 8 and subtracting 3 and then dividing by 7 incorrectly. C halves the correct answer. D comes from using 4d in place of 7d, that is from taking half of n − 1.

2. Q2. If the first and last terms are a and l, the sum of n terms is:

   • A.n/2(a+l)✓
   • B.n(a+l)
   • C.(a+l)/n
   • D.n/2(a−l)
   Solution

   Sₙ=n/2(a+l).

3. Q3. Three numbers are in AP. Their sum is 24 and their product is 440. The numbers are:

   • A.4, 8, 12
   • B.6, 8, 10
   • C.3, 8, 13
   • D.5, 8, 11✓
   Solution

   Taking the numbers as a − d, a, a + d gives 3a = 24 so a = 8; then 8(64 − d²) = 440 gives d² = 9, d = 3, i.e. 5, 8, 11.

4. Q4. The sum of first 15 even natural numbers is: Verify the related AP-sum calculation:

   • A.240✓
   • B.225
   • C.210
   • D.250
   Solution

   2(1+…+15)=15×16=240.

5. Q5. A machine produces 50 units in the first hour and 5 more each hour. Production in 12 hours is:

   • A.930✓
   • B.900
   • C.960
   • D.870
   Solution

   S₁₂=12/2[100+11×5]=930.

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