Question

Given the sequence −2,−8/3,−103,−4,−14/3,... find the recursive formula.

A. a1=−2 and an+1=an+5/3
B. a1=−2 and an+1=an+1/3
C. a1=−2 and an+1=an−2/3
D. a1=−2 and an+1=an−5/3

Answer 1

I suppose the third term should say -10/3, not -103.

Notice that

-2 = -6/3

-4 = -12/3

so that, starting with the first term a(1) = -6/3, the every following term is obtained by subtracting 2/3.

-2 - 2/3 = -6/3 - 2/3 = -8/3

-8/3 - 2/3 = -10/3

-10/3 - 2/3 = -12/3 = -4

and so on.

So the recursive rule is

a(1) = -2,

a(n + 1) = a(n) - 2/3, for n ≥ 1

or C.