Elementary Practical Mathematics for Technical Students

Elementary Practical Mathematics for Technical Students

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This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1905 edition. Excerpt: ... be read off directly also. CHAPTER XIII. ARITHMETICAL PROGRESSION. GEOMETRICAL PROGRESSION. GEOMETRIC MEAN AND ARITHMETIC MEAN. SIMPLE INTEREST. COMPOUND INTER-EST. DISCOUNT. Arithmetical Progression.--Quantities are said to be in arithmetical progression when they increase or decrease by the addition or subtraction of the same quantity. Thus the numbers 1, 2, 3, 4, which increase by the addition of 1 to each successive term; 21, 18, 15, 12, which decrease by the subtraction of 3 from each successive term; a, a+d, a+20l, etc.; and a, a--d, a--20l, increasing or diminishing by the addition or subtraction of a quantity d--are in arithmetical progression. It will be seen that if a be the first term, a+0l the second, a+2d the third, etc., any term, such as the eighth, is equal to a added to d repeated (8-1) times, or a+70l; therefore, if l be the nth or in words, the sum of a number of terms in arithmetical progression is found by multt'plyz'n_q the sum of the first and last terms by half the number of terms. In this form, when the first, last, and number of terms are known, the sum can be found. The sum can also be obtained when the first term and the number of terms are given, as follows: Arithmetic Mean.--The middle term of any three quantities in an arithmetical progression is the arithmetic mean of the other two. Thus if a and b are the two quantities, and A the arithmetic mean, then a, A, and b form three terms of an arithmetical progression, and ' A--a= b-A, Hence the arithmetical mean of two quantities is half their sum. It is always possible between any two given quantities to insert a number of terms such that the whole series are in arithmetical progression. l--a Thus from (i) (i=7: gives the common difference. Ex. 1. Insert 6...show more

Product details

  • Paperback | 88 pages
  • 189 x 246 x 5mm | 172g
  • Rarebooksclub.com
  • United States
  • English
  • black & white illustrations
  • 1236899792
  • 9781236899798