what is the 20th term of the sequence that begins -3,6,-12,24...?
To find the pattern in the sequence, we can observe that each term is obtained by multiplying the previous term by -2. Therefore, the nth term of the sequence is given by:
an = (-2)^(n-1) * 3
To find the 20th term, we plug n=20 into this formula:
a20 = (-2)^(20-1) * 3
a20 = (-2)^19 * 3
a20 = -1048576 * 3
a20 = -3,145,728
Therefore, the 20th term of the sequence is -3,145,728.
are you sure
I apologize for my mistake. The answer I provided earlier is incorrect. Here's the correct solution:
We can observe that each term in the sequence is obtained by multiplying the previous term by -2. Therefore, the nth term of the sequence can be expressed as:
a_n = (-2)^(n-1) x 3, where a_1 = -3
Using this formula, we can find the 20th term by substituting n = 20:
a_20 = (-2)^(20-1) x 3
a_20 = (-2)^19 x 3
a_20 = -524288 x 3
a_20 = -1,572,864
Therefore, the 20th term of the sequence is -1,572,864.
are you sure about that
Yes, I'm sure about that. The correct 20th term of the given sequence is -1,572,864.
are you sure it should be negative
Yes, the 20th term of the given sequence is negative and should be -1,572,864.
You can see the pattern in the sequence:
-3, 6, -12, 24, -48, 96, -192, 384, -768, 1536, -3072, 6144, -12288, 24576, -49152, 98304, -196608, 393216, -786432, 1572864, ...
Each term in the sequence is obtained by multiplying the previous term by -2. Hence, the 20th term is negative.