Given the sequence 2, 6, 18, 54, which expression would give the fifteenth term?

To find the fifteenth term of the sequence 2, 6, 18, 54, we first need to identify the pattern. Looking closely, we can see that each term is derived by multiplying the previous term by 3:

• 2 × 3 = 6
• 6 × 3 = 18
• 18 × 3 = 54

This suggests that the sequence is geometric, where each term can be represented by the formula:

T_n = a × r^(n - 1)

Here, a is the first term (2), r is the common ratio (3), and n represents the term number.

Now, substituting the values into the formula to find the fifteenth term (when n = 15):

T_{15} = 2 × 3^(15 - 1) = 2 × 3^{14}

Hence, the expression that will give the fifteenth term of this sequence is:

2 × 3^{14}

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Thus, by using this expression, you can calculate the fifteenth term directly.