Jared creates a number sequence that’s has a first term of 2 and a second term of 5

Sn = 2+3n

Step-by-step explanation:

Complete question

Jared creates a number sequence that has a first term of 2 and a second of term of 5. Each term after the second is created by subtracting the term before the previous term from twice the previous term. He uses S (t) to denote term number t in his sequence. For example, S (1) =2 and S (2) = 5

Let the sequence be 2, 5,...

We are to find the nth term of the sequence

The nth term of an arithmetic sequence is expressed as

Sn = a+(n-1)d

a is the first term = 2

d is the common difference = 5- 2 = 3

Substitute

Sn = 5 + (n-1)(3)

Sn = 5+3n-3

Sn = 2+3n

Hence the nth term of the sequence is 2+3n