THE MATHEMATICAL THEORY OF INVESTMENT PAET I. ALGEBRAIC INTRODUCTION CHAPTER I PROGRESSIONS 1. Definitions. An arithmetical progression is a succession of terms such that any term may be obtained from the preceding term by the addition of a constant number called the common difference. If the common difference is positive, the progression is said to be increasing; if it is negative, the progression is said to be decreasing. ILLUSTRATIVE EXAMPLES. The progressions 2, 4, 6, 8 and 1, U, 2, U are increasing arithmetical progressions, the first with common difference 2 and the second with common difference ^. The progression ^ ^ ^ ^ ^ _2 is a decreasing arithmetical progression with common difference — 2. A geometrical progression is a succession of terms such that any term may be obtained by multiplying the preceding term by a con- stant number. The constant multiplier by means of which any term is derived from the preceding term is called the ratio. If the ratio is numerically greater than 1, the progression is called an increasing geometrical progression; if it is numerically less than 1, the progression is called a decreasing geometrical progression. 1