5. Divide the dividend by the divisor, and the quotient will be the term sought. NOTE. When the first term of the series is equal to the ratio, the indices must begin with an unit, and the indices added must make the entire index of the term required; and the product of the different terms, found as before, will give the term required. EXAMPLES. 1. The first term of a geometrical series is 2, the number of terms 13, and the ratio 2; required the last term. 1, 2, 3, 4, 5, indices, 2, 4, 8, 16, 32, leading terms. Then 4+4+3+2= index to the 13th term. In this example the indices must begin with 1, and such of them be chosen, as will make up the entire index to the term required. 2. Required the 12th term of a geometrical series, whose first term is 3, and ratio 2. 0, 1, 2, 3, 4, 5, 6, indices. 3, 6, 12, 24, 48, 96, 192, leading terms. Then 6+5= index to the 12th term. And 192x96-18432 dividend. The number of terms multiplied is 2, and 2—1—1 is the power, to which the term 3 is to be raised; but the first power of 3 is 3, and therefore 18432-3-6144 the 12th term required. 3. The first term of a geometrical series is 1, the ratio 2, and the number of terms 23; required the last term. Ans. 4194304. QUESTIONS TO BE SOLVED BY THE TWO PRECEDING PROBLEMS. 1. A person being asked to dispose of a fine 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. 44739241. 5s. 32d. 2. A young man, skilled in numbers, agreed with a farmer to work for him eleven years without any other reward than the produce of one wheat corn 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 increase to be in a ten fold proportion; what quantity of wheat is due for such service, and to what does 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 debt will be discharged in a year, or twelve months, by paying $1 the first month, $2 the second, $ 4 the third, and so on, each succeeding payment being double the last; and what will the last payment be? Ans. The debt is $ 4095 and the last payment $ 2048. SIMPLE INTEREST. INTEREST is the premium, allowed for the loan of money. The sum, which is lent, is called the principal. The sum of the principal and interest is called the amount. Interest is allowed at so much per cent. per annum, which premium per cent. per annum, or interest of 100l. for a year, is called the rate of interest. Interest is of two sorts, simple and compound. Simple Interest is that, which is allowed only for the principal lent. NOTE. Commission, Brokerage, Insurance, Stocks,* and, in general, whatever is at a certain rate, or sum per cent. are calculated like Simple Interest. * Stock is a general name for public funds, and capitals of trading companies, the shares of which are transferable from one person to another. RULE.* 1. Multiply the principal by the rate, and divide the product by 100; and the quotient is the answer for one year. 2. Multiply the interest for one year by the given number of years, and the product is the answer for that time. 3. If there be parts of a year, as months or days, work for the months by the aliquot parts of a year, and for the days by Simple Proportion. EXAMPLES. 1. What is the interest of 4501. for a year, at 5 per cent. per annum? 4501. 5 1,00)22.50 20 10.00 Ans. 221. and %==•5 = 10s; 2. What is the interest of 7201. for 3 years, at 5 per cent, per annum; 3. What is the interest of 1071. for 117 days, at 43 per |