What is the 20th term of the sequence -3, 6, -12, 24
The answer is 1,572,864 i just need to know the math in order to obtain the answer.
That is geometric sequence where firs term a1 = - 2 and common ratio r = - 2
The n-th term of a geometric sequence:
an = a1 ∙ r ⁿ ⁻¹
In this case:
a20 = - 3 ∙ ( - 2 ) ²⁰ ⁻¹ = - 3 ∙ ( - 2 ) ¹⁹ = - 3 ∙ ( - 1 ∙ 2 ) ¹⁹ =
= - 3 ∙ ( - 1 ) ¹⁹ ∙ ( 2 ) ¹⁹ =
- 3 ∙ ( - 1 ) ∙ ( 2 ) ¹⁹ = 3 ∙ 524 288 = 1 572 864
Find the 30th term of the geometric sequence 3, 6, 12, 24, . . . ?
Find the 30th term of the geometric sequence 3, 6, 12, 24, . . . ?
Well, numbers can be quite funny sometimes! Let's take a closer look at this sequence. Each term seems to be doubling in magnitude while alternating signs. So, the pattern goes like this:
-3, (3)6, (-6)12, (12)24...
As you can see, we double the previous term and alternate the sign each time.
To find the 20th term, we need to apply this pattern 19 times because the first term is already given.
Starting with -3, after 19 doublings, we get:
-3, 6, -12, 24, -48, 96, -192, 384, -768, 1536, -3072, 6144, -12288, 24576, -49152, 98304, -196608, 393216, -786432, 1572864.
And voila! The 20th term of the sequence is 1,572,864. Now, isn't that a hilarious number?
To find the 20th term of the given sequence, we can observe that each term is obtained by multiplying the previous term by -2.
We start with the first term, -3. To find the second term, we multiply -3 by -2, which gives us 6.
To find the third term, we multiply the second term, 6, by -2, giving us -12.
We continue this pattern of multiplying each term by -2 to obtain the next term.
So, let's compute the sequence a bit further to find the 20th term:
4th term = -12 * -2 = 24
5th term = 24 * -2 = -48
6th term = -48 * -2 = 96
Continuing this process, we find:
7th term = 96 * -2 = -192
8th term = -192 * -2 = 384
9th term = 384 * -2 = -768
10th term = -768 * -2 = 1536
11th term = 1536 * -2 = -3072
12th term = -3072 * -2 = 6144
...
...
...
19th term = -1,572,864.
Hence, the 20th term of the sequence -3, 6, -12, 24 is -1,572,864.