I don't understand this math at all plz help me

The next term in the sequence is obtained by subtracting 4 from the previous term:

13 = 17 - 4

9 = 13 - 4

5 = 9 - 4

and so on.

Recursively, we can describe the n-th term in the sequence (denoted a(n)) as a function of the (n - 1)-th term:

a(n) = a(n - 1) - 4

starting with a(1) = 17. So we have, for instance,

a(2) = a(1) - 4 = 17 - 4 = 13

We want to find an explicit formula for a(n), meaning we want a way to determine the n-th term only as a function of n, and not any other known term in the sequence. We can iteratively apply the recursive rule above:

a(n) = a(n - 1) - 4

a(n - 1) = a(n - 2) - 4

→   a(n) = (a(n - 2) - 4) - 4 = a(n - 2) - 2×4

a(n - 2) = a(n - 3) - 4

→   a(n) = (a(n - 3) - 4) - 2×4 = a(n - 3) - 3×4

a(n - 3) = a(n - 4) - 4

→   a(n) = (a(n - 4) - 4) - 3×4 = a(n - 4) - 4×4

and so on, down to

a(n) = a(1) - (n - 1)×4

The first term is a(1) = 17, so

a(n) = 17 - 4 (n - 1) = 21 - 4n

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step-by-step explanation: