Question

Find at least three different sequences beginning with the terms 1, 2, 4 whose terms are generated by a simple forμla or rule.

a) True
b) False

Answer 1

Three different sequences starting with 1, 2, 4 could be a geometric sequence (1, 2, 4, 8, 16, ...), a quadratic sequence (1, 2, 4, 7, 11, ...), or an exponential plus constant sequence (1, 2, 4, 5, 6, ...).

Step-by-step explanation:

The question asks for at least three different sequences that begin with the terms 1, 2, 4 and follow a simple rule or formula. Here are three examples:

• Geometric Sequence: The sequence 1, 2, 4, 8, 16, 32, ... is a geometric sequence where each term is twice the previous term (multiplied by 2).
• Quadratic Sequence: The sequence 1, 2, 4, 7, 11, 16, ... follows a quadratic pattern where the n-th term can be represented as 0.5n^2 - 0.5n + 1.
• Exponential Plus Constant Sequence: The sequence 1, 2, 4, 5, 6, 7, ... is created by taking the 2^n sequence for the first three numbers, and then adding 1 to each subsequent term starting with the fourth term.

Each of these sequences starts with 1, 2, 4 and has a simple formula or rule determining the later terms.