Math & Logic Puzzle Challenge - Number Sequences & Arithmetic

The pattern follows: 3 × 4 = 12, 12 × 13 = 156, 156 × 157 = 24,492. Each multiplier (4, 13, 157) follows the pattern of multiplying the previous number by a larger factor. Specifically: multiply by (previous number + 1) to get the next term. None of the other options (25000, 312, 24459) follow this mathematical relationship.

This sequence shows the squares of prime numbers in order: 1² = 1, 2² = 4, 3² = 9, 5² = 25, 7² = 49, 11² = 121. The primes are 1, 2, 3, 5, 7, 11 (note: 1 is technically not prime, but included in this pattern). The next prime after 11 is 13, so 13² = 169 would logically follow. Option D (2) doesn't fit, and 132 and 1900 are not squares of primes.

The differences between consecutive terms increase by 11 each time: 21-10=11, 43-21=22, 76-43=33, so the next difference should be 44, giving 76+44=120. The pattern is adding 11, then 22, then 33, then 44 (multiples of 11). Options 130, 150, and 165 don't fit this consistent difference pattern.

The sequence shows an unclear pattern with differences of +4, +6, +6. If we look for a logical continuation, one possible pattern is that each difference is double the position (4, 6, 8, 10, 12...), which would give 18+8=26, 26+10=36, 36+12=48. Another interpretation gives 30 as the answer, but the pattern is ambiguous. This question has a weak mathematical foundation.

The pattern follows consecutive even number additions: 1+2=3, 3+4=7, 7+6=13, 13+8=21, and 21+10=31. The increment increases by 2 each time (2, 4, 6, 8, 10), making this a second-order arithmetic progression.

This is a simple arithmetic progression with a common difference of 3. Each term increases by 3: 1+3=4, 4+3=7, 7+3=10, and 10+3=13. The missing number is 10, maintaining the constant increment pattern.

The sequence consists of the squares of consecutive odd numbers: 1^2=1, 3^2=9, 5^2=25, 7^2=49, 9^2=81. The next term is 11^2=121, followed by 13^2=169. 100 is an even square, while 88 and 77 are not perfect squares.

The pattern involves adding the sum of the digits of the current number to itself: 13+(1+3)=17, 17+(1+7)=25, 25+(2+5)=32. Following this, 32+(3+2)=37. Other options do not follow this consistent arithmetic progression based on digit summation.

This is an alternating sequence. Sequence 1: 2, 7, 12 (+5). Sequence 2: 8, 10, 12 (+2). The next number belongs to Sequence 1: 12 + 5 = 17. Distractors like 13 or 16 do not follow the established patterns.

Basic addition: 1 + 1 = 2. The other options like 11 are results of string concatenation rather than mathematical addition.

Basic addition: 2 + 2 = 4. The other options like 22 or 44 are either concatenations or incorrect multiplications.

In the range of integers from 0 to 10, the only number containing the digit 9 is 9 itself. Thus, there is exactly one 9. The statement is true.

In mathematics, the set of whole numbers typically includes 0 and all positive integers (0, 1, 2, 3...). Therefore, it is true that zero is a whole number.

The binomial expansion of (1-x)^(-1) gives the infinite geometric series 1 + x + x² + x³ + ... for |x| < 1. Option D correctly shows this pattern without factorials in denominators. Options A and B show trigonometric series (cosine and sine respectively) with factorial denominators, while option C incorrectly includes a factorial denominator in the x² term.