What is the 20th term of the sequence that begins with −2, 4, -8, 16
ANSWER CHOICES:
A)2,097,152
B)524,288
C)-524,288
D)1,048,576
To find the 20th term of the sequence, we can use the formula for the nth term of a geometric sequence:
nth term = first term * common ratio^(n-1)
In this sequence, the first term is -2 and the common ratio is -2 (-2 * -2 = 4, 4 * -2 = -8, -8 * -2 = 16).
Let's substitute the values into the formula to find the 20th term:
20th term = -2 * (-2)^(20-1)
= -2 * (-2)^19
Calculating (-2)^19:
(-2)^19 = -524,288
Now let's substitute this value back into the equation:
20th term = -2 * (-524,288)
= -1,048,576
Therefore, the 20th term of the sequence is -1,048,576.
The correct answer is D) 1,048,576.
To find the 20th term of the sequence −2, 4, -8, 16, we need to determine the pattern in the sequence and then apply it to find the desired term.
In this sequence, each term is obtained by multiplying the previous term by -2. Therefore, the pattern is that each term is double the magnitude of the previous term but opposite in sign (negative if the previous term is positive, and positive if the previous term is negative).
Using this pattern, we can find the 20th term:
-2
4 = -2 * (-2)
-8 = 4 * (-2)
16 = -8 * (-2)
-32 = 16 * (-2)
64 = -32 * (-2)
And so on...
Now we can keep applying the pattern until we reach the 20th term. Let's continue until we find it:
128 = 64 * (-2)
-256 = 128 * (-2)
512 = -256 * (-2)
-1024 = 512 * (-2)
2048 = -1024 * (-2)
-4096 = 2048 * (-2)
Finally, we have:
8192 = -4096 * (-2)
Therefore, the 20th term of the sequence is 8192.
None of the answer choices provided match the correct answer of 8192.
a = -2
r = -2
T20 = ar^19 = 2^20 = (D)