hi could anyone help me with this please :?

Question

: Consider the arithmetic sequence, Xn , such that, X3=9 , X9=33

Answer 1

'Arithmetic' means that the increase is regular (same difference between each step).

step 3 = 9
step 9 = 33
difference of 24 for 6 steps = 4 per step

sequence begins:
1, 5, 9, 13, 17, 21, 25, 29, 33, 37


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'Geometric' means that the ratio is the same at each step.

For 6 steps, the ratio would have been 33/9 = 3.66666...
For 1 step, it would have been the sixth root of 3.66666
approx. 1,24178
(from n3 to n9):
,,, 9, 11.176..., 13.878..., 17.233688..., 21.4..., 26.57..., 33,

There are many other kinds (hyperbolic, exponential...)

Answer 2

in X3=9 : x=3

in X9=33 : x=3.666666666666666666666