Final answer:
To find the 10th term of the geometric sequence 10, -20, 40,..., we first determine the common ratio by dividing the second term by the first term, obtaining -2. We then apply the formula for the nth term of a geometric sequence, which gives us -5120 as the 10th term.
Step-by-step explanation:
The question asks us to find the 10th term of the geometric sequence 10, -20, 40,... A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a constant called the common ratio (r). To find the common ratio, we divide the second term by the first term:
r = (-20) / 10
= -2
Now, we use the formula for the nth term of a geometric sequence:
an = a1 * r^(n-1)
For the 10th term (n=10), the formula becomes:
a10 = 10 * (-2)^(10-1)
Calculating this, we get:
a10 = 10 * (-2)^9
a10 = 10 * (-512)
a10 = -5120
Therefore, the 10th term of the sequence is -5120.