 Quandaries and Queries Name: grant Who is asking: Student Level of the question: Secondary Question: n+7, 2n-0.5, 4n. Find the next 5 terms of each one and explain the sequence in words Hi Grant, Rather than doing one of your homework question I am going to do a similar problem. I am going to look at 3n - 2 The letter n stands for the number of the term in the sequence. For example For the first term, n = 1; so 3n - 2 = 3 1 - 2 = 3 - 2 = 1 For the second term, n = 2; so 3n - 2 = 3 2 - 2 = 6 - 2 = 4 For the third term, n = 3; so 3n - 2 = 3 3 - 2 = 9 - 2 =7 For the fourth term, n = 4; so 3n - 2 = 3 4 - 2 = 12 - 2 = 10 etc. So the value of the firsat four terms arre 1, 4, 7, 10 If you are given the term 3n - 2 and you want the next five terms then these are the terms numbered n + 1; n + 2; n + 3; n + 4 and n + 5 Thus the values are 3(n + 1) - 2 = 3n + 3 - 2 = 3n + 1 3(n + 2) - 2 = 3n + 6 - 2 = 3n + 4 3(n + 3) - 2 = 3n + 9 - 2 = 3n + 7 etc To explain the sequence in words I would say that the value of a term is 3 time the term number minus 2. Thus, for example, the value of the ninth term is 3 9 - 2 = 27 - 2 = 25 Penny   