Final answer:
The 10th term of the geometric sequence 2, 6, 18, ... is 118,098. Each term is obtained by multiplying the previous term by 3.
Step-by-step explanation:
The given sequence is 2, 6, 18, ....
To find the term 118,098 in the sequence, we can observe that each term is obtained by multiplying the previous term by 3. So the common ratio, r, is 3.
We can express the terms of the sequence using the formula a₁₂₃₄ = a₁r^(n-1), where a₁ is the first term, r is the common ratio, and n is the number of the term we want to find.
Setting up the equation, we have:
2 * 3^(n-1) = 118,098
Dividing both sides by 2:
3^(n-1) = 59,049
Since 3^5 = 243 and 3^6 = 729, we know that n-1 is between 5 and 6. We can use logarithms to solve for n-1:
n-1 = log(base 3) of 59,049 = 9
n = 10
Therefore, the 10th term of the sequence is 118,098.