Question

find a sub 15 for the sequence -1.5,3, -6...

Answer 1

The sequence is as follows:\[-\frac{ 3 }{ 2 }, 3, -6, ....\]
What pattern does the sequence follow?

Answer 2

Geometric?

Answer 3

\[-\frac{ 3 }{ 2 },\frac{ 6 }{ 2 },-\frac{ 12 }{ 2 }, \frac{ 24 }{ 2 }, -\frac{ 48 }{ 2 },...\]The sequence follows a linear equation. See how you're just multiplying each term by -2? You can figure out an equation for the whole series.

Answer 4

Woah. Mind = Blown!

Answer 5

\[y=-2x\]
Is that it?

Answer 6

It's usually described as something along the lines of \[a_{n}=-\frac{3}{2}(-2)^{n}\]

Answer 7

I'm sorry, it might be a little advanced for your level, you probably wouldn't need to find the equation, but it goes something like this:
\[a_n = 3 (-1)^n 2^{n-2}\]
I think for your level, your teacher probably just wanted you to count to the 15th term.
if \[a _{1}=-1.5\]
\[a _{2}=3\]
\[a _{3}=-6\]
count up to \[a _{15}=?\] and check it with the equation I gave you, plugging in n=15.

Answer 8

So I should come to the answer of 49152 correct?

Answer 9

I think you went 1 too many.
1) -1.5
2) 3
3) -6
4) 12
5) -24
6) 48
7) -96
8) 192
9) -384
10) 768
11) -1536
12) 3072
13) -6144
14) 12288
15) -24576
16) 49152

Answer 10

\[a_{15}=3(−1)^{15}2^{15−2}=-24576\]
Tell your teacher you solved for that equation in your head, maybe they'll graduate you early, haha

Answer 11

Haha! I wish!

Answer 12

@chrismoon looks like \[a _{n } = \frac{ 3 }{ 4 }(-2)^n \] should work too. Though the standard form for geometric (which i was trying to remember when i worked that out) is \[a _{n} = a _{1} r ^{n-1}\] where a1 is the first term and r is the common ratio, which would be:
\[a _{n} = -1.5 (-2) ^{n-1}\] which works too.

Answer 13

@SOSAlgebra6629 have you done the standard form for geometric sequence? This form: \[a _{n} = a _{1} r ^{n-1}\]

Answer 14

No. What is that?

Answer 15

Yea, they're the same equation, I just didn't simplify. Since\[2^{n-2}=\frac{ 2^n }{ 2^2 }\]and \[(-1)^{n}2^n=(-2)^n\]
My original equation can be reduced to yours.

Answer 16

Wait a second, is the a sub 1 the first number in the sequence? Is the r the rate of change?

Answer 17

^yes to both. r is the common ratio which is -2.

Answer 18

if you've done geometric sequences you've prob used it\[\large a _{n} = a _{1} r ^{n-1}\]a sub n just means the n-th term.