Problem: Let a sequence {un​} be defined by the relation un​+1−un​=3+4(n−1), n=1,2,3,…, and u1​=5. If un​ is expressed as a polynomial in n, the algebraic sum of its coefficients is:
Answer Choices:
A. 3
B. 4
C. 5
D. 6
E. 11
Solution:
By "telescopic" addition we obtain un+1​−u1​=3n+4⋅21​(n−1)(n−1+1). Since u1​=5,un+1​=2n2+n+5. Therefore, un​=2(n−1)2+(n−1)+5=2n2−3n+6.
Since 2−3+6=5, the correct answer is (C).
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