1969 AMC 12 Problem 32

Question

Let a sequence

\{u_n\}

be defined by

u_1=5

and the relation

u_{n+1}-u_n=3+4(n-1),

n=1,

2,

3,

\ldots.

If

u_n

is expressed as a polynomial in

n,

the algebraic sum of its coefficients is:

3

4

5

6

11

The sum of a polynomial’s coefficients is its value at

n=1

The problem already gives

u_1

For any polynomial

p(n),

the sum of its coefficients is

p(1).

Here the polynomial represents

u_n,

and the initial condition gives

u_1=5.

Therefore the coefficient sum is

5.

Therefore, the correct answer is C.

Problem 32 in other years