Hello, 13373l1t3!

They asked for the "recursive" formula.

But if they want, say, the 21st term, we'd better have a "closed" form.

4. Write a recursive formula to generate each sequence.

Then find the indicated term.

. Find the 10th term.

The sequence increases by 4 at each stage.

The recursive formula is: .

(Each term is the preceding term plus 4.)

The closed formula is: .

Therefore: .

. Find the 12th term.

Each term is one-tenth of the preceding term.

The formula is: .

Therefore: .

. Find the 15th term.

The terms decrease by 2.31

The formula is: .

Therefore: .

. Find the 8th term.

Each term is times the preceding term.

The formula is: .

Therefore: .

. Find the 21st term.

This is a sneaky one!

Here is my thought process . . .

The numerators seems to be all 1's.

Then how come the first term has a numerator of 0 ?

Then it hit me . . . the numerators are: .

. . and the denominators are all 6's !!

Get it? .We have: .

. . andthatis why the sequence begins: .

The formula is: .

Therefore: .

. Find the 15th term.

Each term is to a power.

The formula is: .

Therefore: .