I need to write a sequence for which f(3) = 1/4

Answer 1

f(3) = 1/4 means you want the 3rd term in a sequence to be 1/4.

There are an infinite number of possibilities for this. First you have to ask yourself if you want to have a geometric sequence (where a term is multiplied by some number to get the next term) or you want an arithmetic sequence (where a term is added by some number to get to the next term).

Let's arbitrarily pick a geometric sequence.

Now, we have to ask, what number do we want to multiply by?

Let's arbitrarily multiply each term by 1/2.

To go backwards to the second term, we have to do the opposite of multiplying by 1/2 (which is divide by 1/2 or multiply by 2 - both are the same thing). So if the 3rd term is 1/4, then the second term is 1/2 (1/4 x 2 = 1/2) and the first term is 1 (1/2 x 2 = 1)

So the sequence is 1, 1/2, 1/4 . . .

To write an equation for a geometric sequence write f(n) = (initial term)(multiplier)^n-1 so it would be f(n) = 1(1/2)^n-1

Answer 2

A sequence is a list of numbers separated by commas that have either a common difference (arithmetic), or a common ratio (geometric), or possibly a quadratic relation.

f(x) is notation for a function. It may or may not express and sequence.

Restate your question with correct terms.