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2, 5, 8, 11, 14, ___
Reasoning: The series follows a pattern of adding 3 to the previous number to obtain the next number. Starting with 2, we add 3 repeatedly to get the subsequent terms: 2 + 3 = 5, 5 + 3 = 8, 8 + 3 = 11, and so on. Therefore, the missing number is 17.
1, 4, 9, 16, 25, ___
Reasoning: The series represents the sequence of perfect squares. The first term is 1, which is the square of 1. The second term is 4, which is the square of 2. The third term is 9, which is the square of 3, and so on. Hence, the next term is 36, which is the square of 6.
3, 6, 12, 24, 48, __
Reasoning: In this series, each term is obtained by multiplying the previous term by 2. Starting with 3, we multiply by 2 repeatedly to get the subsequent terms: 3 * 2 = 6, 6 * 2 = 12, 12 * 2 = 24, and so on. Therefore, the missing term is 96.
1, 3, 6, 10, 15, ___
Reasoning: This series follows the pattern of adding consecutive positive integers. The first term is 1, the second term is obtained by adding 1 to the first term (1 + 1 = 2), the third term is obtained by adding 2 to the second term (2 + 2 = 4), and so on. Therefore, the missing term is obtained by adding 5 to the previous term: 15 + 5 = 21.
0, 1, 1, 2, 3, 5, ___
Reasoning: This series is known as the Fibonacci sequence. Each term is obtained by adding the two previous terms. Starting with 0 and 1, we add them to get the third term (0 + 1 = 1), add the second and third terms to get the fourth term (1 + 1 = 2), and so on. Therefore, the missing term is obtained by adding the two previous terms: 3 + 5 = 8.
2, 4, 8, 16, 32, ___
Reasoning: Each term in the series is obtained by multiplying the previous term by 2. Starting with 2, we multiply by 2 repeatedly to get the subsequent terms: 2 * 2 = 4, 4 * 2 = 8, 8 * 2 = 16, and so on. Therefore, the missing term is 64.
7, 14, 28, 56, 112, ___
Reasoning: In this series, each term is obtained by multiplying the previous term by 2. Starting with 7, we multiply by 2 repeatedly to get the subsequent terms: 7 * 2 = 14, 14 * 2 = 28, 28 * 2 = 56, and so on. Hence, the missing term is 224.
10, 7, 4, 1, -2, __
Reasoning: The series follows a pattern of subtracting 3 from the previous number to obtain the next number. Starting with 10, we subtract 3 repeatedly to get the subsequent terms: 10 - 3 = 7, 7 - 3 = 4, 4 - 3 = 1, and so on. Therefore, the missing number is -5.
12, 9, 6, 3, 0, ___
Reasoning: Each term in the series is obtained by subtracting 3 from the previous term. Starting with 12, we subtract 3 repeatedly to get the subsequent terms: 12 - 3 = 9, 9 - 3 = 6, 6 - 3 = 3, and so on. Hence, the missing term is -3.
1, 4, 9, 16, 25, 36, ___
Reasoning: The series represents the sequence of perfect squares. Each term is obtained by squaring the consecutive positive integers. The first term is 1, which is the square of 1. The second term is 4, which is the square of 2. The third term is 9, which is the square of 3, and so on. Therefore, the missing term is 49, which is the square of 7.
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