The New Complete System of Arithmetick

2. A man travelled 6 days; the first day he went miles, and each day doubling his day's travel, his last day's ride was 128 miles; How far did he go in the whole ?

3. A gentleman dying, left 5 sons; to whom he be queathed his eftate as follows, viz to his youngest son 1000l.; to the eldest 50621. 10s. and ordered that each son should exceed the next younger by the equal ratio of 1; What did the several legacies amount to ? 5062,5-1000

1,5-1

+5062,5=131871. 10s. Ans.

PROB. 4. Given the extremes and ratio, to find the num ber of terms.

RULE.--Divide the greatest term by the leaft; find what power of the tatio is equal to the quotient; then, add to the index of that power, and the sum will be the number of terms

Or, Subtract the logarithm* of the least term from that of the greatest; divide the remainder by the logarithm of the ratio. and add 1 to the quotient.

EXAMPLE.

If the least term be 2, the greatest term 4374, and the ratio. 3, What is the number of terms ?

Divide by the least term=2)4374=greatest term.

3X3X3X3X3X3X3=Quo, 2187=7th power, then 7+1=8 the Auf.

* Logarithms are artificial numbers, the addition of which anfwers to multiplication of whole numbers, and fubtraction to division,

PROB. 5 Given the leaft term, the ratio, and the sum of

the feries, to find the last term.

RULE.-Multiply the sum of the series by the ratio, lefs; to that product add the first term, and the result divided by the ratio, will give the last term.

EXAMPLE.

If the ist term be 2, the ratio 3, and the sum of the

feries 6560; What is the last term ?

3-1×6560+2

=4374 Ans.

SIMPLE INTEREST.

Interest is a premium allowed by the borrower of any sum of money to the lende, according to a certain rate per cent. agreed on, which by law is stated at 61. that is, 6 for the ufe of 100l. for one year. Principal is the money lent.

Rate is the fum per cent. agreed on.
Amount is the principal and interest added together.
Interest is of two forts, fimple and compound.
Simple interest is that, which is allowed for the prin-

cipal lent only

Note. The rules for simple interest ferve also to calculate commiffion, brokerage, insurance, purchafing stocks, or any thing else rated at fo much per cent.

GENERAL

GENERAL RULE.

1. Multiply the principal by the rate, and divide the product by ico (or which is the fame, cut off the two right hand figures in the pounds which must be reduced to the lowest denomination, each time cutting off as at first) and the quotient will be the answer for one year.

2. For more years than one, multiply the interest of one year by the given number of years, and the product will bede 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 the Rule of Shree Direct, or (which is sufficiently exact for common use, allowing 30 days to the month) take aliquot parts of the fame.