Olympiad Test: Patterns in Mathematics - 1 - Class 6 MCQ

Let us check the pattern:
From 2 → 4, the number is multiplied by 2.
From 4 → 8, again multiplied by 2.
From 8 → 16, multiplied by 2.
Therefore, the rule of the sequence is: "Multiply the previous number by 2."
So the next number = 16 × 2 = 32.

The sequence represents perfect squares:
1 = 1²
4 = 2²
9 = 3²
16 = 4²
25 = 5²
The next term should be 6² = 36.

This sequence follows the rule n² + 1.
For n=1: 1² + 1 = 2
For n=2: 2² + 1 = 5
For n=3: 3² + 1 = 10
For n=4: 4² + 1 = 17
For n=5: 5² + 1 = 26
For n=6: 6² + 1 = 37
So the missing number is 26.

Even numbers are divisible by 2.
Option A: 1, 3, 5, 7 → odd numbers.
Option B: 2, 4, 6, 8 → all even numbers, correct.
Option C: multiples of 5, not all even.
Option D: multiples of 3, not all even.
Therefore, the correct sequence of even numbers is 2, 4, 6, 8.

Triangular numbers are formed by adding consecutive natural numbers:
1
1 + 2 = 3
3 + 3 = 6
6 + 4 = 10
10 + 5 = 15
So the first five triangular numbers are 1, 3, 6, 10, 15.

The sequence doubles each time:
3 × 2 = 6
6 × 2 = 12
12 × 2 = 24
24 × 2 = 48
48 × 2 = 96
Thus, the missing number is 48.

The sequence is letters of the alphabet, skipping one each time:
A, C, E, G …
After G comes I (since H is skipped).
Therefore, the next letter is I.

Odd numbers: 1, 3, 5, 7, 9.
Sum = 1 + 3 + 5 + 7 + 9 = 25.
There is also a formula: sum of first n odd numbers = n².
Here, n=5 → 5² = 25.
So the answer is 25.

The pattern is n(n+1).
1 × 2 = 2
2 × 3 = 6
3 × 4 = 12
4 × 5 = 20
5 × 6 = 30
6 × 7 = 42
So the missing number is 30.

Option A: 2, 3, 5, 7, 11 → all are prime numbers.
Option B: 1 (not prime), 9 (not prime).
Option C: even numbers, not all prime.
Option D: multiples of 5, not prime.
So the correct sequence is 2, 3, 5, 7, 11.