Final answer:
The 20th term of the sequence is found using the formula for a geometric series. By applying the common ratio of 3 to the first term, which is 2, the 20th term is calculated as 2 multiplied by 3 to the power of 19. The correct option is D) $3^{19}$.
Step-by-step explanation:
The original question asks what is the 20th term of the sequence 2, 6, 18, 54.... To find the 20th term, we can first determine the pattern of the sequence. This sequence is a geometric sequence because each term is multiplied by the same number (the common ratio) to obtain the next term. In this case, the common ratio is 3, as each term is three times the preceding term. The formula for the nth term of a geometric series is a_n = a_1 × r^{(n-1)}, where a_1 is the first term, r is the common ratio, and n is the term number.
Using the formula to find the 20th term:
a_{20} = 2 × 3^{(20-1)} = 2 × 3^{19}
Comparing our result with the options provided, we can see that the correct option is D) $3^{19}$, because the factor of 2 is already accounted for in the first term of the sequence and the rest of the exponentiation stems from the multiplications by the common ratio.