Final answer:
The 6th term of the geometric sequence with a common ratio of 1/3 and first term of 2 is found using the geometric sequence formula and is calculated to be 2/243.
Step-by-step explanation:
To find the 6th term of the geometric sequence with a common ratio of 1/3 and a first term of 2, we use the formula for the nth term of a geometric sequence, which is an = a1 × r(n-1), where a1 is the first term, r is the common ratio, and n is the term number. In this case, a1 is 2, r is 1/3, and n is 6. Substituting these values into the formula gives us a6 = 2 × (1/3)(6-1), which simplifies to a6 = 2 × (1/3)5. Calculating the power, we get a6 = 2 × (1/243), which gives us a6 = 2/243 as the 6th term of the sequence.