ABSTRACT
Problem 1. Determine (a) the ninth, and (b) the sixteenth term of the series 2, 7, 12, 17, . . .
2, 7, 12, 17, . . . is an arithmetic progression with a common difference, d, of 5
(a) The n0th term of an AP is given by aCn1d Since the first term a D 2, d D 5 and n D 9 then the 9th term is:
2 C 9 15 D 2 C 85 D 2 C 40 D 42 (b) The 16th term is:
2 C 16 15 D 2 C 155 D 2 C 75 D 77
Problem 2. The 6th term of an AP is 17 and the 13th term is 38. Determine the 19th term
The n0th term of an AP is aC n 1d The 6th term is: aC 5d D 17 1 The 13th term is: aC 12d D 38 2 Equation (2) equation (1) gives: 7d D 21, from which, d D 21
7 D 3
Substituting in equation (1) gives: aC15 D 17, from which, a D 2 Hence the 19th term is:
aC n 1d D 2 C 19 13 D 2 C 183 D 2 C 54 D 56
Problem 3. Determine the number of the term whose value is 22 in the series 2
1 2
, 4, 51 2
, 7, . . .
