What is the 13th term of the geometric sequence
8, −16, 32, −64, …
The first term of the geometric sequence is 8 and the common ratio is -2.
To find the 13th term, we can use the formula for the nth term of a geometric sequence:
Tn = ar^(n-1)
where Tn is the nth term, a is the first term, r is the common ratio, and n is the term number.
Plugging in the values for this problem, we get:
T13 = 8 * (-2)^(13-1)
= 8 * (-2)^12
= 8 * 4096
= 32768
Therefore, the 13th term of the geometric sequence is 32768.
To find the 13th term of the geometric sequence, we need to determine the formula for the sequence first.
In a geometric sequence, each term is found by multiplying the previous term by a constant value called the common ratio.
In this case, the common ratio is -2 because each term is obtained by multiplying the previous term by -2.
To find the formula for the 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 position of the term we want to find.
In this case, a_1 = 8 and r = -2, so the formula becomes:
a_n = 8 * (-2)^(n-1)
To find the 13th term (a_13), we substitute n = 13 into the formula:
a_13 = 8 * (-2)^(13-1)
= 8 * (-2)^12
= 8 * 4096
= 32768
Therefore, the 13th term of the geometric sequence is 32768.
To find the 13th term of a geometric sequence, we need to identify the first term (a) and the common ratio (r). In this case, the first term is 8 and the common ratio is -2.
The formula to find the nth term of a geometric sequence is given as:
an = a * r^(n-1)
Now, let's substitute the values into the formula:
a13 = 8 * (-2)^(13-1)
Simplifying the exponent:
a13 = 8 * (-2)^12
Next, solve the exponent:
(-2)^12 = 4096
Substitute the value back into the formula:
a13 = 8 * 4096
Multiply:
a13 = 32768
Therefore, the 13th term of the given geometric sequence is 32768.