CEOMETRICAL TROCRESSION. l8l 



2. Required the 12th term of a geometrical series, 

 wliose first term is 3, and ratio 2. 



o> ij 2, 3, 4, 5, 6, indices. 

 ' 3, 6, 12, 24, 48, 96, 192, leading 'terms. 

 Then 6-^^ zz index to the 12th term. 

 And 192 X96ZZ 18432 zz dividend. 

 The number of terms multiplied is 2, and 2 — iini is 

 the power to which the term 3 is to be raised ; but the 

 first power of 3 is 3, and therefore 18432 -7- 3 zz 6 144 the 

 1 2th term required. 



3. The first term of a geometrical series is i, the ratio 

 2; and the number of terms 23 5 required the last term. 



Ans. 4194304. 



QUESTIONS 



TO BE SOLVED BY THE TWO PRECEDING PROBLEMS. 



1. A person, being asked to dispose of a fme horse, said 

 he would sell him on condition of having one farthing for 

 the first nail in his shoes, 2 farthings for the second, one 

 penny for the third, and so on, doubling the price of every 

 nail to 32, the number of nails in his four shoes : what 

 would the horse be sold for at that rate ? 



Ans. 4473924I. 5s. 3|d. 



2. A young man, skilled in numbers, agreed with a 

 farmer to work for him eleven years without any other re- 

 ward than the produce of one wheat com for the first year, 

 and that produce to be sowed the second year, and so on 

 from year to year till the end of the time, allowing the in- 

 crease to be in a tenfold proportion : what qirantity of 

 wheat is due for such service, and to what docs it amount 

 at a dollar per bushel ? 



Ans. 226056^ bushels, allowing 7680 wheat corns to 

 be a pint -, and the amount is 226056— dollars. 



3. What 



