Class 8 Patterns in Numbers — practice questions with answers
Number System · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.
1. The even numbers form the pattern 2, 4, 6, 8, ... where the nth term is 2n. The sum of the first n even numbers follows the pattern 2 = 2, 2 + 4 = 6, 2 + 4 + 6 = 12, which equals n(n+1). What is the sum of the first 12 even numbers?
A132
B144
C156
D168
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Answer: C) 156
The sum of the first n even numbers is n(n+1); for n = 12 it is 12 x 13 = 156.
2. What is the next term in the pattern: 1, 8, 27, 64, ?
A100
B112
C125
D144
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Answer: C) 125
These are cubes: 1³, 2³, 3³, 4³; the next is 5³ = 125.
3. Find the next term: 1, 4, 13, 40, ?
A121
B111
C131
D242
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Answer: A) 121
Each term is 3 times the previous plus 1: 40 x 3 + 1 = 121.
4. A magician asks Priya to pick any number, multiply it by 3, then look at the units digit pattern of multiples of 3: 3, 6, 9, 2, 5, 8, 1, 4, 7, 0. This cycle of units digits repeats every 10 multiples. What is the units digit of the 25th multiple of 3?
A3
B5
C7
D9
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Answer: B) 5
25th multiple of 3 is 75; its units digit is 5. (The cycle position 25 mod 10 = 5, giving 5.)
5. A clever pattern: 1 = 1, 1 + 2 = 3, 1 + 2 + 3 = 6, ... the sum of the first n numbers. Manoj wants the sum of all whole numbers from 1 to 20. Using the pattern 2n(n+1), what total does he get?
A190
B420
C230
D210
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Answer: D) 210
Sum from 1 to n is 2n(n+1); for n = 20 it is 220×21 = 210.