Question

Find a pattern for each sequence. Use the pattern to show the next two terms.
3. -3, 6, -12, 24, -48, … 4. 1, 5, 30, 210, 1680, …

Answer 1

You can often track this sort of thing down with successive differences.

-3 - 3 = -6 = -2*3
6 - (-3) = 9 = +3*3
-12 - 6 = -18 = -6*3 = -2*3*3 <== Multiplied previous by -2
24 - (-12) = 36 = +12*3 = 2*2*3*3 <== Multiplied previous by -3
-48 - 24 = -72 = -24*3 = -2*2*2*3*3 <== Multiplied previous by -2

Maybe the differences are not very helpful on this one. You do just have to play around with it.

3
-3 = -1(3)
6 = -2*(-3)
-12 = -2(6)
24 = -2(-12)
-48 = -2(24)

Again, except for the 1st one, we're there.

Just toy with it. You'll think of something.

Occasionally, there will be two sequences interwoven.

3, 6, 24 ==> 3, 3*2, 3*8 ==> 3*2^0, 3*2^1, 3*2^3, maybe 3*2^6 is next?
-3, -12, -48 ==> -3, -3*4. -3*16, maybe -3*64 is next?

Answer 2

you have to do all the steps with diffenrt numbers