Explain why the sequence is exponential or linear and write the rule; 48, 24, 12, 6, 3…

Answer 1

Hi Mira. The sequence is linear, because you are dividing by 2 each time. The rule would be “divide by two.”

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Answer 2

A linear sequence follows a constant difference rule. This means that each next term can be determined by adding some specific number (which can be negative) to the previous term. For example, 2, 5, 8, 11, 14... would be a linear sequence, as each term can be found by adding 3 to the previous one. An exponential sequence follows a constant ratio rule. This means that each next term can be determined by multiplying some specific number (which can be negative and/or less than 1) to the previous term. For example, 54, 18, 6, 2, 2/3... is an exponential sequence, since each term can be found by multiplying the previous one by 1/3.

Looking at the sequence we are given, 48-24=24, so if it is a linear sequence, each term is equal to the previous one minus 24. 24-24=0, which is not the next term, so this is not a linear sequence. 48/24=2, so 48/2=24. This means if we have an exponential sequence, each term is equal to the previous term divided by 2, or times 1/2. 24/2=12, which is the next term. Likewise, 12/2=6, and 6/2=3, so the sequence follows this rule nicely, making it an exponential sequence.