[i really need in advance] *dont forget starting value*: write the recursive formulas forc=11, 8, 5, 2, -1d= 7, 11, 15, 19, 23e= 12, 8, 4, 0, -4f= 2, 8, 14, 20, 26,

Sequences c, d, e, f in the problem statement

The corresponding recursive relations describing them

Several tests can be run to determine the nature of the sequence you're dealing with. To check for an arithmetic sequence, look at the differences from one term to the next.

Here, the differences are constant, so all of these sequences are arithmetic sequences. The recursion relation only requires you add the difference to the previous term. The initial term is always the first one.

Sequence c

The second term minus the first term is 8-11 = -3, so the difference is -3.

c[1] = 11

c[n] = c[n-1] - 3

Sequence d

The second term minus the first term is 11-7 = 4, so the difference is 4.

d[1] = 7

d[n] = d[n-1] + 4

Sequence e

The second term minus the first term is 8-12 = -4, so the difference is -4.

e[1] = 12

e[n] = e[n-1] - 4

Sequence f

The second term minus the first term is 8-2 = 6, so the difference is 6.

f[1] = 2

f[n] = f[n-1] +6