Discussion
The number of terms in the sequence 2,6,18,...,1458 is
Answer: E
There are 7 terms.
The sequence is a G.P. with first term 2 and common ratio 3, so the \(n\)th term is \(2 \cdot 3^{n-1}\).
\[ \begin{aligned} 2 \cdot 3^{n-1} &= 1458 \\ 3^{n-1} &= 729 = 3^{6} \\ n &= 7 \end{aligned} \]
Check by listing: 2, 6, 18, 54, 162, 486, 1458, which is seven terms. 8 counts one too many, and the larger options treat the sequence as arithmetic.
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