Question

HELP ME PLEASE

Write the following Arithmetic Sequence using a Recursive Formula: an = -5 + 2(n - 1)

1) a1 = -5, an = an-1 + 2
2) a1 = 2, an = an+1 - 5
3) a1 = 2, an = an-1 - 5
4) a1 = -5, an = an+1 + 2

Answer 1

1) a1 = -5, a(n) = a(n-1) + 2

Explanation:

The explicit formula for an arithmetic sequence can be written ...

an = a1 +d(n -1)

The corresponding recursive formula is ...

a(1) = a1, a(n) = a(n -1) +d

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Comparing the above explicit formula to the one you're given, you see that ...

a1 = -5, d = 2

Using these values in the recursive formula gives you ...

a(1) = -5, a(n) = a(n-1) +2