Find the 10th term of the geometric sequence 10, -50, 250,
To find the 10th term of a geometric sequence, we need to determine the common ratio and use the formula
a_n = a_1 * r^(n-1),
where a_n represents the n-th term, a_1 represents the first term, r represents the common ratio, and n represents the position of the term we are interested in.
In this case, we can find the common ratio by dividing any term by the previous term. Let's use the first two terms:
-50 / 10 = -5
Now, we can use the formula to find the 10th term:
a_10 = 10 * (-5)^(10-1)
= 10 * (-5)^9
= 10 * (-1953125)
= -19531250
Therefore, the 10th term of the geometric sequence 10, -50, 250 is -19,531,250.
To find the 10th term of a geometric sequence, we first need to determine the common ratio (r) of the sequence. The ratio (r) is found by dividing any term of the sequence by its previous term.
Let's take the second term (-50) and divide it by the first term (10):
r = -50 / 10 = -5
Now that we have the common ratio (r = -5), we can use the formula for finding the nth term of a geometric sequence:
An = A1 * r^(n-1)
In this formula, An represents the nth term, A1 represents the first term, r represents the common ratio, and n represents the position of the term that we want to find.
Given A1 = 10, r = -5, and we want to find the 10th term (n = 10), we can substitute the values into the formula:
A10 = 10 * (-5)^(10-1)
Simplifying the exponent:
A10 = 10 * (-5)^9
Now, calculate the value of (-5)^9:
A10 = 10 * (-5 * -5 * -5 * -5 * -5 * -5 * -5 * -5 * -5)
The negative signs in the exponent alternate, so we have an even number of negatives, which means the result will be positive. Calculating (-5)^9 gives:
A10 = 10 * (-1953125)
Multiplying 10 by -1953125:
A10 = -19,531,250
Therefore, the 10th term of the geometric sequence 10, -50, 250 is -19,531,250.
dang. 10*(-5)^(n-1)
or -2(-5)^n
a = 10
r = -5
The nth term is 2*(-5)^(n-1)
so plug in n=10