Series & Patterns
105 questions available
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Q1.What is a and b in the given sequence: a, 13, 9, 3, -5, -15, b?
Correct Answer: B
The sequence decreases by 4 each time (13,9,3,-5? actually differences vary), and solving the pattern gives a = 15 and b = -27.
Q2.What is the next term in the series? 11, 20, 35, 56, 83
Correct Answer: B
Correct answer is B: 116
Q3.121, 144, 169, 196, what comes next?
Correct Answer: B
The sequence consists of squares of consecutive integers: 11^2 = 121, 12^2 = 144, 13^2 = 169, 14^2 = 196. The next term is 15^2 = 225.
Q4.What will be the next term in the pattern? 2, 4, 8, 16, ______?
Correct Answer: C
Each term is multiplied by 2 to yield the next term: 2*2=4, 4*2=8, 8*2=16. The next term is 16*2=32.
Q5.Find the sum: 2*1^2 + 4*2^2 + 6*3^2 + ... + 20*10^2
Correct Answer: D
Rewrite terms: 2*n*n^2 = 2*n^3. Total sum = 2 * Sum_{n=1}^{10} n^3 = 2 * [10*(10+1)/2]^2 = 2 * [55]^2 = 2 * 3025 = 6050.
Q6.What is the 10th term of the series? 2*1^2 + 4*2^2 + 6*3^2 + ...
Correct Answer: C
The nth term expression is 2*n * n^2 = 2*n^3. For the 10th term (n=10): 2 * (10)^3 = 2 * 1000 = 2000.
Q7.Complete the number series: 4, 6, 12, 14, 28, 30, ____?
Correct Answer: B
Pattern alternates: Add 2, then Multiply by 2. 4+2=6, 6*2=12, 12+2=14, 14*2=28, 28+2=30. Next: 30*2=60.
Q8.Find the missing number: 1, 3, 7, 15, 31, 63, ______?
Correct Answer: C
Pattern is: Next = Prev * 2 + 1. 1*2+1=3, 3*2+1=7, 7*2+1=15, 15*2+1=31, 31*2+1=63. Next: 63*2+1=127.
Q9.Find the missing number: 5, 11, 23, 47, ?
Correct Answer: A
Pattern is: Next = Prev * 2 + 1. 5*2+1=11, 11*2+1=23, 23*2+1=47. Next term is 47*2+1=95.
Q10.Find the next term: 5, 10, 20, 40, ?
Correct Answer: C
This is a geometric sequence with ratio r=2. Each term is doubled. Next term = 40 * 2 = 80.
Q11.Complete the series: 6, 3, 12, 6, 24, ______?
Correct Answer: C
Pattern is alternating operations: Divide by 2, then Multiply by 4. 6/2=3, 3*4=12, 12/2=6, 6*4=24, 24/2=12.
Q12.What is the next term in the sequence: 2, 1, 3, 4, 7, 11?
Correct Answer: B
Each term is the sum of the preceding two terms: 2+1=3, 1+3=4, 3+4=7, 4+7=11. The next term is 7+11=18.
Q13.Complete the series: 1, 1, 8, 4, 27, 9 _____?
Correct Answer: A
The series alternates cubes and squares: 1^3 = 1, 1^2 = 1, 2^3 = 8, 2^2 = 4, 3^3 = 27, 3^2 = 9. Next is 4^3 = 64.
Q14.Which number will complete the number series? 2, 5, 12, 23, 38, 57, ____?
Correct Answer: A
The differences between consecutive terms are +3, +7, +11, +15, +19. These differences increase by +4 each time. The next difference is 19 + 4 = 23. Thus, the next term is 57 + 23 = 80.
Q15.Complete the sequence: 2 / 4 → 4 / 16 → 16 / 256 → ?
Correct Answer: A
Each numerator is the square of the previous numerator: 2^2=4, 4^2=16, 16^2=256. Each denominator is the square of the previous denominator: 4^2=16, 16^2=256, 256^2=65536. So, the next term is 256 / 65536.
Q16.What is the next number in the series: 15, 45, 75, 105?
Correct Answer: C
The difference between consecutive terms is constant at +30. The next term is 105 + 30 = 135.
Q17.What is the next number in the sequence: 15, 30, 45, ____?
Correct Answer: B
The sequence increases by +15 each time. The next term is 45 + 15 = 60.
Q18.Complete the series: 43, 53, 63, ____?
Correct Answer: B
The terms increase by a constant difference of +10. The next term is 63 + 10 = 73.
Q19.What is the next number in this sequence: 1, 3, ____, 7, 11?
Correct Answer: A
The sequence is 1, 3, 5, 7, 11. It consists of numbers increasing by 2 (odd numbers) but 9 is skipped, or alternatively, differences are +2, +2, +2, +4. The missing term is 5.
Q20.Complete the series: 3 | 3 | 3 | 6 | 3 | 9 | 3 | ____?
Correct Answer: C
The series alternates: 3 is placed at odd positions (1st, 3rd, 5th, 7th). The numbers at even positions (2nd, 4th, 6th) increase by 3: 3 -> 6 -> 9. The next even-positioned term should be 9 + 3 = 12.