The first term of a geometric sequence is -2 and the common ratio is 3. What is the 12th term of the sequence?
term(12) = ar^11
= (-2)(3^11)
= -2 (3^11) = -354294
Why did the geometric sequence refuse to share its 12th term?
Because it wanted to keep its growth rate a secret!
But in all seriousness, to find the 12th term of a geometric sequence with a first term of -2 and a common ratio of 3, you can use the formula:
nth term = a * r^(n-1)
Plugging in the values:
12th term = -2 * 3^(12-1)
Simplify the exponent:
12th term = -2 * 3^11
And finally, calculate the answer:
12th term ≈ -1458
To find the 12th term of the geometric sequence, you can use the formula:
\[T_n = a \times r^{(n-1)}\]
where:
- \(T_n\) is the nth term of the sequence,
- \(a\) is the first term of the sequence, and
- \(r\) is the common ratio.
In this case, the first term (\(a\)) is -2 and the common ratio (\(r\)) is 3. We want to find the 12th term (\(T_{12}\)). Plugging these values into the formula, we get:
\[T_{12} = -2 \times 3^{(12-1)}\]
Now, let's calculate the 12th term step by step:
1. Subtract 1 from 12: \(12 - 1 = 11\)
2. Calculate \(3^{11}\). This can be done by multiplying 3 by itself 11 times: \(3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3 = 177147\)
3. Multiply -2 by 177147: \(-2 \times 177147 = -354294\)
Therefore, the 12th term of the geometric sequence is \(-354294\).
To find the 12th term of a geometric sequence given the first term and the common ratio, we can use the formula:
nth term = a * r^(n-1)
where:
- nth term is the term we want to find (in this case, the 12th term),
- a is the first term of the sequence, and
- r is the common ratio of the sequence.
Given that the first term (a) is -2, and the common ratio (r) is 3, we can substitute these values into the formula:
12th term = -2 * 3^(12-1)
Now we just need to evaluate the right side of the equation:
12th term = -2 * 3^11
= -2 * 177147
= -354294
Therefore, the 12th term of the geometric sequence is -354294.