Question

Write down the terms denoted by the question marks in the following sequences:

1) 0,2,4,2,?,10,12,14
2) 3,5,8,13,?,34,55,?
3) 2,4,10,28,?,?,730
4) 5,11,29,83,?,731

Answer 1

The missing terms in the numerical sequences are determined by recognizing the patterns they follow, such as alternating operations, Fibonacci sequence, and multiplicative and additive rules. For the presented sequences, the missing terms are 8, 21, 89, 82, and 245, respectively.

Step-by-step explanation:

The sequences presented by the student are numerical patterns where the succeeding terms are generated based on a rule or a function applied to the previous terms.

1. The pattern seems to be alternating between adding and subtracting 2. Therefore, the term between 4 and 10 should be 8 (4 + 2=6 and then sequentially - 2+ 2).
2. This sequence resembles the Fibonacci sequence, where each term is the sum of the two preceding ones. Hence, the missing terms are 21 (13 + 8) and 89 (55 + 34).
3. The pattern in this series is multiplicative and additive, where each term after the first is obtained by multiplying the previous term by an increasing number and then adding another increasing number. For example, 2 multiplied by 1 plus 2 is 4, 4 multiplied by 2 plus 2 is 10, and so on. So, the missing terms are 82 and 244 calculated through the pattern.
4. Similar to the third sequence, this one follows a multiplicative and additive pattern. The missing term before 731 would be 245 applying the identified rule.

For each of these sequences, recognizing the underlying pattern is crucial for determining the missing terms. Different sequences can follow arithmetic, geometric, Fibonacci-like, or other complex rules, and identifying the correct sequence type is essential for solving these problems.