1969 AHSME Problems/Problem 32
Problem
Let a sequence be defined by and the relationship If is expressed as a polynomial in , the algebraic sum of its coefficients is:
Solution
Note that the first differences create a linear function, so the sequence is quadratic.
The first three terms of the sequence are , , and . From there, a system of equations can be written. Solve the system to get , , and . The sum of the coefficients is .
Note: Solving the system is extra work, as the answer is described by the first equation. The sum of the coefficients () is just 5 by the first equation.
See also
1969 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 31 |
Followed by Problem 33 | |
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