The first term of a geometric sequence is -400, and the common ratio is
−12
.
What is the 10th term of the sequence?
To find the 10th term of a geometric sequence, we can use the formula:
Term_n = a * r^(n-1)
where Term_n is the nth term of the sequence, a is the first term, r is the common ratio, and n is the position of the term we want to find.
In this case, the first term (a) is -400, the common ratio (r) is -12, and we want to find the 10th term (n=10).
Plugging these values into the formula, we get:
Term_10 = -400 * (-12)^(10-1)
Simplifying the exponent, we have:
Term_10 = -400 * (-12)^9
Calculating the value of the exponent:
-12^9 = -12 * -12 * -12 * -12 * -12 * -12 * -12 * -12 * -12
= 17,179,869,184
Plugging this value back into the formula:
Term_10 = -400 * 17,179,869,184
Calculating the result:
Term_10 = -6,871,947,673,600
Therefore, the 10th term of the sequence is -6,871,947,673,600.
To find the 10th term of the geometric sequence, you can use the formula:
\[a_n = a_1 \times r^{(n-1)}\]
where:
- \(a_n\) is the nth term,
- \(a_1\) is the first term, and
- \(r\) is the common ratio.
Given that the first term (\(a_1\)) is -400 and the common ratio (\(r\)) is -12, we can substitute these values into the formula:
\[a_{10} = -400 \times (-12)^{(10-1)}\]
Now, let's calculate the 10th term.
To find the 10th term of a geometric sequence, you can use the formula:
a_n = a_1 * r^(n-1)
Where:
a_n is the nth term of the sequence
a_1 is the first term of the sequence
r is the common ratio
n is the position of the term we want to find
In this case, the first term (a_1) is -400, the common ratio (r) is -12, and we want to find the 10th term (n = 10).
Now, substitute these values into the formula and solve for a_n:
a_n = -400 * (-12)^(10-1)
= -400 * (-12)^9
Calculating this value, we get:
a_n ≈ -400 * (-12)^9
≈ -400 * (-5,159,780,352)
Simplifying further, we get:
a_n ≈ 2,063,912,140,800
Therefore, the 10th term of the sequence is approximately 2,063,912,140,800.