Answer:
In a geometric sequence, each term is found by multiplying the previous term by a constant value called the common ratio (r).
In this case, the first term (a₁) is 2, and the common ratio (r) can be found by dividing any term by its preceding term. Let's calculate it:
r = 6 / 2 = 3
Now, to find the 15th term (a₅₊₁₋₅), we can use the formula:
aₙ = a₁ * r^(n-1)
Substituting the values, we have:
a₁ = 2
r = 3
n = 15
a₁₅ = 2 * 3^(15-1)
Calculating the exponent first:
3^(15-1) = 3^14 = 4782969
Now, substituting this value back into the formula:
a₁₅ = 2 * 4782969
a₁₅ = 9565938
Therefore, the 15th term of the geometric sequence 2, 6, 18, ... is 9565938.
Explanation: