Sequences
Subject 1: Explicit definition of a sequence as a
function of n.
 Level 1 : Calculate a_{9}
in a given sequence
 Level 2 : Express a_{n3}
in terms of n
 Level 3 : Find the location of a given term
Subject 2: Recursive definition of a sequence.
 Level 1 : Calculate a_{2},
a_{3}, .. , a_{6}
 Level 2 : Calculate a_{8}
given a_{10}
 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 a_{1} and d
 Level 2 : Calculate a_{n}
by a_{3} and d
 Level 3 : Calculate a_{n}
by a_{3} and a_{12}
 Level 4 : Find two successive terms whose sum is
172
 Level 5 : Find n such that a_{n}
is greater than a_{7}
by 66
 Level 6 : Insert a sequence between two numbers
 Level 7 : Calculate S_{k+3},
S_{n+2} by a_{1} and d
 Level 8 : Calculate the sum a_{12}
+ a_{13} + ... + a_{n}
Subject 4: Geometric progression.
 Level 1 : Calculate a_{n}
by q and a_{1}
 Level 2 : Calculate a_{n}
by q and a_{5}
 Level 3 : Calculate a_{1}
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 a_{1}
