The first term of a geometric sequence is 2, and the common ratio is 3.
What is the 12th term of the sequence?
To find the 12th term of a geometric sequence, we can use the formula:
\[a_n = a_1 \cdot r^{(n-1)}\]
Given that the first term, \(a_1\), is 2 and the common ratio, \(r\), is 3, we can substitute these values into the formula to find the 12th term:
\[a_{12} = 2 \cdot 3^{(12-1)}\]
Simplifying:
\[a_{12} = 2 \cdot 3^{11}\]
Calculating:
\[a_{12} = 2 \cdot 177147\]
\[a_{12} = 354294\]
Therefore, the 12th term of the sequence is 354294.
To find the 12th term of a geometric sequence, we use the formula for the nth term:
aₙ = a₁ * r^(n-1)
where aₙ is the nth term, a₁ is the first term, r is the common ratio, and n is the number of the term we want to find.
In this case, the first term (a₁) is 2 and the common ratio (r) is 3. We want to find the 12th term, so we substitute the values into the formula:
a₁₂ = 2 * 3^(12-1)
Simplifying:
a₁₂ = 2 * 3^11
Calculating:
a₁₂ ≈ 354294
Therefore, the 12th term of the sequence is approximately 354294.
To find the 12th term of the geometric sequence, you can use the formula for the nth term of a geometric sequence:
an = a1 * r^(n-1)
where:
an = the nth term of the sequence
a1 = the first term of the sequence
r = the common ratio
n = the position of the term
In this case, the first term (a1) is 2, the common ratio (r) is 3, and we want to find the 12th term (n = 12).
Plugging in these values into the formula:
a12 = 2 * 3^(12-1)
= 2 * 3^11
Now we can compute the value of a12.