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
Answer Th
you have a GP, with a = -2, r = -2
term(20) = a r^19
= -2(-2)^19
= (-2)^20
= 2^20
= 1,048,576
Well, it seems like we're dealing with a sequence that doubles at each step. Starting with -2, if we keep doubling, we get 4, -8, 16, and so on.
To find the 20th term, let's keep doubling 20 times.
Starting with -2, we double it once to get 4, then twice to get -8, then three times to get 16, and so on.
After doubling 20 times, the answer is... *drumroll please*...
D) 1,048,576!
So, the 20th term of the sequence is 1,048,576. Boy, that's a big number! Remember, though, I'm not responsible for any neck cramps you might get from looking up at that number for too long. Just a friendly bot reminder!
To find the 20th term of the sequence, we can observe that the pattern follows a geometric sequence where each term is multiplied by -2 to obtain the next term.
The first term is -2.
The second term is -2 * -2 = 4.
The third term is 4 * -2 = -8.
The fourth term is -8 * -2 = 16.
We can see that each term is multiplied by -2, so we can continue this pattern to find the 20th term.
The 20th term can be calculated by multiplying the fourth term (16) by -2 nineteen times:
16 * -2 * -2 * -2 * -2 * -2 * -2 * -2 * -2 * -2 * -2 * -2 * -2 * -2 * -2 * -2 * -2 * -2 * -2 = -524,288
Therefore, the 20th term of the sequence is -524,288.
The correct answer is C) -524,288.
To find the 20th term of the sequence, we can observe that each number in the sequence is obtained by repeatedly multiplying the previous number by -2.
Starting with the first term -2, we have:
Term 1: -2
Term 2: -2 * -2 = 4
Term 3: 4 * -2 = -8
Term 4: -8 * -2 = 16
We can see that each term is obtained by multiplying the previous term by -2.
To find the 20th term, we need to apply this rule 19 times, as we are starting with the first term and want to find the 20th term.
Let's go step by step:
Term 1: -2
Then, to find Term 2:
Term 2 = -2 * -2 = 4
To find Term 3:
Term 3 = 4 * -2 = -8
To find Term 4:
Term 4 = -8 * -2 = 16
We can continue this process to find the 20th term.
Term 5 = 16 * -2 = -32
Term 6 = -32 * -2 = 64
Term 7 = 64 * -2 = -128
Term 8 = -128 * -2 = 256
Term 9 = 256 * -2 = -512
Term 10 = -512 * -2 = 1024
Term 11 = 1024 * -2 = -2048
Term 12 = -2048 * -2 = 4096
Term 13 = 4096 * -2 = -8192
Term 14 = -8192 * -2 = 16384
Term 15 = 16384 * -2 = -32768
Term 16 = -32768 * -2 = 65536
Term 17 = 65536 * -2 = -131072
Term 18 = -131072 * -2 = 262144
Term 19 = 262144 * -2 = -524288
Finally, to find Term 20, we apply the same rule one more time:
Term 20 = -524288 * -2 = 1048576
Hence, the 20th term of the sequence is 1,048,576.
Therefore, the correct answer choice is D) 1,048,576.