Let an be the sum of the first n positive odd integers.

(a) list out at least the first 4 terms of the sequences. be sure to use proper notation.

(b) give the closed/explicit formula for this sequence. be sure to use proper notation.

(c) give the recursive formula for this sequence. be sure to use proper notation.

A) The first 4 terms of the sequences are: , , and .

B) An explicit formula for this sequence can be written as:

C) A recursive formula for this sequence can be written as:

Step-by-step explanation:

A) You can find the firs terms of this sequence simply selecting an odd integer and summing the consecutive 3 ones:

(a.1)

B) Observe the sequence of odd numbers 1, 3, 5, 7, 9, 11, 13(...).

You can express this sequence as:

(b.1)

If you merge the expression b.1 in a.1, you obtain the explicit formula of the sequence:

(a.1)

(b.2)

(b.3)

(b.s)

C) The recursive formula has to be written considering an initial term and an N term linked with the previous term. You can see an addition of 8 between a term and the next one. So you can express each term as an addition of 8 with the previous one. Therefore, if the first term is 16:

(c.s)

207/8 is the right