Question

How to find the nth term of a sequence if the common difference between the terms are not the same? for example, 1,-2,3,-4...

Answer 1

did you just throw that out?

Answer 2

What do you mean ?

Answer 3

Because it does not seem to have any closed form that I know of

Answer 4

oh okay, it was in this question sheet my lecturer gave. how about this sequence, 11,8,13,6,15.. the common difference isnt the same, how do i find the nth term of this sequence ?

Answer 5

11 8 13 6 15
diff -3 5 -7 9 = ( 2n-1)(-1)^n (n=1,2,3,......)

Maybe putting that into Summation might work

Answer 6

\[11+\sum _{n=1}^{N-1} (2n+1)(-1)^n\]

seem to work

Answer 7

Sometimes you have to just try and spot the pattern. For example:\[2,4,8,16,32,\ldots\]could be re-written as:\[2^1,2^2,2^3,2^4,2^5,\ldots\]which leads us to believe a closed form might be:\[a_n=2^n\]

Answer 8

The first sequence you have:\[1,-2,3,-4\ldots\]could be:\[a_n=(-1)^{n+1}n\]

Answer 9

we cannot use the formula for the nth term, which is Tn= a + (n-1)d, to find the nth term of a sequence if the common difference between the terms are not the same ?

Answer 10

\[11+\sum _{n=1}^{N-1} (2n+1)(-1)^n\]
solved out to be
\[10-(-1)^N N\]

Answer 11

could you show me how you go that 10-(-1)^n (n) ?

Answer 12

Well it requires solving that Sum which I can't do by hand