Help with this geometric sequence

It's gibberish.

May I politely suggest you proofread questions before posting them?

Hi sorry for that i will remember to do so in the future. Please look below your reply for an image of the table. Thank you

It would have made more sense (and be easier to refer to) if you had transcribed the values into text.

Anyhow, the values you have posted do not form a geometric sequence.

Well what form of sequence or series do you think it is then?

you can make a gp for even seconds and odd seconds

Looking at the table, if you are expliclty saying that the even terms take the form $a_{2n} =2 \times 2^n$, and the odd terms $a_{2n+1} = 3 \times 2^n$, then I think

$a_n = (2 + \frac{1}{2}(1- (-1)^n)(\frac{3}{\sqrt{2}} - 2))\sqrt{2^n}$

will work.

wouldn't it be easier to consider 2 gp instead of the complicated general term you provided ?

Yes, but since I gave the formula for both the GP as well and OP asked for an explicit formula...

If you dont mind me asking, how did you calculate the explicit formula ?

If you start from

$a_n = 2 \times 2^{n/2}$ (which is correct for even n), and then look at what happens for odd n, you find you need to replace the first 2 with $\frac{3}{\sqrt{2}}$ to get it to work for odd n.

That is, you need to add $\frac{3}{\sqrt{2}} - 2$ to the first 2 when n is odd.

Then I just used that $\frac{1}{2}(1-(-1)^n)$ is 0 for n even and 1 for n odd.

[And if you were wondering - part of the point of doing this was to illustrate that sometimes asking for a single formula is not the most sensible thing to do...]

Looking at the table, if you are expliclty saying that the even terms take the form $a_{2n} =2 \times 2^n$, and the odd terms $a_{2n+1} = 3 \times 2^n$, then I think

$a_n = (2 + \frac{1}{2}(1- (-1)^n)(\frac{3}{\sqrt{2}} - 2))\sqrt{2^n}$

will work.

Thank you very much for your effort. But feeding this does not seem to generate the right answers.

Perhaps this sequence is too complicated to work with.

Just tried it in Excel, it works fine.

Too complicated for you, possibly.

Relax buddy. I just added that line because I didn't want to seem disrespectful.

And feeding this in a scientific calculator does not give the right results even after triple checking. And I would encourage everyone who is reading to try it out and report back here so mine is not a fluke.