1)
-1, 5, -7, 17, -31, 65, ...
the relationship between the terms: +6 (-1+6=5), -12 (5-12=-7), +24, -48, +96
I came up with 6(-2)^(n-1) (-1)^(n-1) for that part, but do not know how to incorporate it back into the overall formula
2)
2, -7, 8, -13, 14, -19, ...
the relationship between the terms: -9, +15, -21, +27, -33
I came up with 3(3+2(n-1)) (-1)^n; and then the same situation as above
another relationship, if one takes out the negative signs: +5, +1, +5, +1, +5...
Is there a "way" to do this systematically?
Thanks in advance.
-1, 5, -7, 17, -31, 65, ...
the relationship between the terms: +6 (-1+6=5), -12 (5-12=-7), +24, -48, +96
I came up with 6(-2)^(n-1) (-1)^(n-1) for that part, but do not know how to incorporate it back into the overall formula
2)
2, -7, 8, -13, 14, -19, ...
the relationship between the terms: -9, +15, -21, +27, -33
I came up with 3(3+2(n-1)) (-1)^n; and then the same situation as above
another relationship, if one takes out the negative signs: +5, +1, +5, +1, +5...
Is there a "way" to do this systematically?
Thanks in advance.
-
the first thing i see when i look at the first one is that they're all part of the 2-series (2^n) with a deviation of 1 (which changes for with the sign on the term). this leads to:
(-1)^n*(2^n)+(-1)^n
the second one is a bit harder though, and i cant really come up with anything else than a series that depends on the previous term:
a_n=a_(n-1)+3(2n+1)*(-1)^n, a_0=2
that's all i can think of for now, hope it helps,
oh, and unfortunately, there isn't a systematic way of doing this, it's just guesswork...
(-1)^n*(2^n)+(-1)^n
the second one is a bit harder though, and i cant really come up with anything else than a series that depends on the previous term:
a_n=a_(n-1)+3(2n+1)*(-1)^n, a_0=2
that's all i can think of for now, hope it helps,
oh, and unfortunately, there isn't a systematic way of doing this, it's just guesswork...