The first term of a geometric sequence is -400, and the common ratio is
−1/2
.
What is the 10th term of the sequence?
To find the 10th term of the geometric sequence, we can use the formula for the nth term of a geometric sequence:
a_n = a_1 * r^(n-1)
where a_n is the nth term, a_1 is the first term, r is the common ratio, and n is the term number.
In this case, the first term is -400, the common ratio is -1/2, and we want to find the 10th term.
a_10 = -400 * (-1/2)^(10-1)
= -400 * (-1/2)^9
= -400 * (-1/512)
= -400/512
= -0.78125
Therefore, the 10th term of the sequence is -0.78125.
To find the 10th term of the geometric sequence, we can use the formula:
\(a_n = a_1 \cdot r^{(n-1)}\)
Where:
\(a_n\) = the nth term of the sequence
\(a_1\) = the first term of the sequence
\(r\) = the common ratio
\(n\) = the position of the term we want to find
Given that:
\(a_1 = -400\)
\(r = -1/2\)
\(n = 10\)
We can substitute these values into the formula:
\(a_{10} = -400 \cdot (-1/2)^{(10-1)}\)
Simplifying:
\(a_{10} = -400 \cdot (-1/2)^9\)
\(a_{10} = -400 \cdot (-1/512)\)
\(a_{10} = 800/512\)
\(a_{10} = 1.5625\)
Therefore, the 10th term of the sequence is 1.5625.
To find the 10th term of the geometric sequence, we can use the formula:
term(n) = first term * common ratio^(n-1)
Given that the first term is -400 and the common ratio is -1/2, we substitute these values into the formula:
term(10) = -400 * (-1/2)^(10-1)
Now, we simplify the expression:
term(10) = -400 * (-1/2)^9
To calculate (-1/2)^9, we can simplify it step by step:
(-1/2)^9 = -1^9 / 2^9
Since any number raised to the power of 9 is the same number, we have:
(-1)^9 / 2^9 = -1 / 2^9
Now, we can calculate the expression:
term(10) = -400 * (-1/2)^9
= -400 * (-1 / 2^9)
= -400 * (-1 / 512)
= 400/512
= 25/32
Therefore, the 10th term of the sequence is 25/32.