Sequences

Subject 1: Explicit definition of a sequence as a function of n.

• Level 1 : Calculate a₉ in a given sequence
• Level 2 : Express a_n-3 in terms of n
• Level 3 : Find the location of a given term

Subject 2: Recursive definition of a sequence.

• Level 1 : Calculate a₂, a₃, .. , a₆
• Level 2 : Calculate a₈ given a₁₀
• Level 3 : Express a_n+5 in terms of a_n+4
• Level 4 : Express a_n+3 in terms of a_n+1

Subject 3: Arithmetic progression.

• Level 1 : Calculate a_n by a₁ and d
• Level 2 : Calculate a_n by a₃ and d
• Level 3 : Calculate a_n by a₃ and a₁₂
• Level 4 : Find two successive terms whose sum is 172
• Level 5 : Find n such that a_n is greater than a₇ by 66
• Level 6 : Insert a sequence between two numbers
• Level 7 : Calculate S_k+3, S_n+2 by a₁ and d
• Level 8 : Calculate the sum a₁₂ + a₁₃ + ... + a_n

Subject 4: Geometric progression.

• Level 1 : Calculate a_n by q and a₁
• Level 2 : Calculate a_n by q and a₅
• Level 3 : Calculate a₁ and q by a_n and a_m
• Level 4 : Find three consecutive terms
• Level 5 : Insert a sequence between two numbers
• Level 6 : Exponential growth and decay
• Level 7 : Calculate S_n by q and a₁