## Mathematical Topics: Sequences Subject 1: Explicit definition of a sequence as a function of n. Level 1 : Calculate a9 in a given sequence Level 2 : Express an-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 an+5 in terms of an+4 Level 4 : Express an+3 in terms of an+1 Subject 3: Arithmetic progression. Level 1 : Calculate an by a1 and d Level 2 : Calculate an by a3 and d Level 3 : Calculate an by a3 and a12 Level 4 : Find two successive terms whose sum is 172 Level 5 : Find n such that an is greater than a7 by 66 Level 6 : Insert a sequence between two numbers Level 7 : Calculate Sk+3, Sn+2 by a1 and d Level 8 : Calculate the sum a12 + a13 + ... + an Subject 4: Geometric progression. Level 1 : Calculate an by q and a1 Level 2 : Calculate an by q and a5 Level 3 : Calculate a1 and q by an and am Level 4 : Find three consecutive terms Level 5 : Insert a sequence between two numbers Level 6 : Exponential growth and decay Level 7 : Calculate Sn by q and a1        (C) Copyright 2000 MathKal Educational Software Ltd.