Final answer:
The 12th term of the geometric sequence 2, 10, 50, is found by using the common ratio (5) in the formula for the nth term of a geometric sequence, resulting in a value of 488281250.
Step-by-step explanation:
To find the 12th term of the geometric sequence 2, 10, 50, we need to determine the common ratio and use the formula for the nth term of a geometric sequence, which is a_n = a_1 × r^{(n-1)}, where a_n is the nth term, a_1 is the first term, and r is the common ratio.
For the given sequence, a_1 = 2, and the common ratio r can be found by dividing the second term by the first term: r = 10 / 2 = 5. Now, using the formula:
a_{12} = 2 × 5^{(12-1)}
a_{12} = 2 × 5^{11}
a_{12} = 2 × 244140625
a_{12} = 488281250
So, the 12th term of the geometric sequence is 488281250.