Question

check your understanding
the first three terms of a sequence are shown.
4,8,12,...
complete the statements.
a rule for the sequence could be where
using the
rule, the next two terms of the sequence
each term is 2 times the previous term
each term is the previous term minus 4
each term is 4 plus the previous term

Explanation:

Step1: Analyze the sequence

The given sequence is \(4, 8, 12, \dots\). Let's check the differences between consecutive terms. \(8 - 4 = 4\) and \(12 - 8 = 4\). So the common difference is 4.

Step2: Evaluate each rule

• For "each term is 2 times the previous term": \(4\times2 = 8\), \(8\times2 = 16

eq12\), so this rule is incorrect.

• For "each term is the previous term minus 4": \(4 - 4 = 0

eq8\), so this rule is incorrect.

• For "each term is 4 plus the previous term": \(4 + 4 = 8\), \(8 + 4 = 12\), which matches the given sequence. So this is the correct rule.

Step3: Find the next two terms

Using the rule "each term is 4 plus the previous term", the next term after 12 is \(12 + 4 = 16\), and the term after 16 is \(16 + 4 = 20\).

Answer:

The rule for the sequence is "each term is 4 plus the previous term". The next two terms of the sequence are 16 and 20.