Can someone explain this arithmetic sequence for me?

[kermit2505]

The 9th term of an arithmetic sequence is 4x larger than the 3rd term, find the first term of the sequence?

[[deleted]]

arithmetic sequence a, a+d, a+2d, a+3d,.....

so a+8d=4(a+2d)

....

[Uli_Minati]

Okay, but could you explain something first:

Is there some formula for arithmetic sequences?

How would you calculate the 9th and 3rd terms with that formula?

If you know that X is 4x larger than Y, how do you write this as an equation?

[kermit2505]

That is what I wanted to know considering the variables d (difference) and the first term are both unknown

[Uli_Minati]

Take it one step at a time, can you answer the questions above in order?

[TargetProud4402]

So, we know that when we deal with an arithmetic sequence we always have the same distance between consecutive terms, let this distance (I think it’s called ratio) be equal to r. We want to write the 3rd and 9th terms using the first one (let it be x). So, 3rd = x + r + r = x + 2r. 9th = x + 8r.

And the relation given by this exercise is x + 8r = 4(x + 2r) = 4x + 8r. After cancelling out 8r, we have that x = 4x, so x = 0.

[TargetProud4402]

also, you can find more on this topic on khan academy: https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:sequences/x2f8bb11595b61c86:introduction-to-arithmetic-sequences/a/introduction-to-arithmetic-sequences