Question

The explicit formula u(n) = -17 + 24n, where u(1) = 7, find the recursive formula for u(n).

A.
u(1) = 7 and u(n + 1) = u(n) + 24, for n = 1, 2, 3, . . .

B.
u(1) = 7 and u(n + 1) = u(n) + 7, for n = 1, 2, 3, . . .

C.
u(1) = 7 and u(n + 1) = 7u(n) + 24, for n = 1, 2, 3, . . .

D.
u(1) = 7 and u(n + 1) = 24u(n) + 7, for n = 1, 2, 3, . . .

Answer 1

given u(n) = -17 + 24n, substitute n+1 fo n:

u(n+1) = -17 + 24(n+1) = 7 + 24n

Now add and subtract u(n) like this (net result would be 0) and simplify:

u(n+1) = u(n) - (-17+24n) + 7 + 24n =>
n(n+1) = u(n) + 17 - 24n + 7 + 24n =>
n(n+1) = u(n) + 24

That is answer A.