Sequences & Series Solutions
Quality-audited sequence and series problems from Zhejiang high-school exams with full derivations and rubrics.
6 problems
Problem 1: Find the general formula of
Let be the sum of the first terms of the sequence . Given , and (1) Find the general formula of . (2) If , find the sum of the first terms of .
Problem 2: Prove that is a square-recursive sequence, and that is a geometric sequence
If a sequence satisfies , then is called a "square-recursive sequence". For the given sequence , , and the point lies on the graph of where is a positive intege
Problem 3: Find the general formula of
Let be the sum of the first terms of an arithmetic sequence , and define Given and . (1) Find the general formula of . (2) Let be the sum of the first terms of
Problem 4: find the value of
Inserting the sum of any two adjacent terms into a sequence is called one "sum-growth" operation; inserting the product of the two adjacent terms is called one
Problem 5: Find the general formulas of and
Let be the sum of the first terms of an arithmetic sequence , with . A geometric sequence satisfies , . (1) Find the general formulas of and . (2) Find the sum
Problem 6: Find the general formula of
Let be the sum of the first terms of the sequence . Suppose and . (1) Find the general formula of . (2) If find , the sum of the first terms of .