5.

A man threshed wheat 9 days for a farmer, and agreed to receive but 8 wheat corns for the firft day's work, 64 for the fecond, and fo on in an eight fold portion; I demand what his 9 day's labour amounted to, rating the wheat at 5s per bufhel ?*

pro

Amount=781. (os. 5d.

6. An ignorant fop wanting to purchase an elegant houfe; a facetious gentleman told him he had one which he would fell him on thefe moderate terms, viz. that he fhould give him a penny for the first door, zd. for the fecond, 4d. for the third, and fo on, doubling at every door, which were 36 in all; it is a bargain, cried the fimpleton, and here is a guinea to bind it; Pray what would the houfe have coft him?

An!.

7.

·X1=68719476735d.=2863311531. 18.

(3d.

A young fellow, well fkilled in numbers, agreed with a rich farmer to ferve him to years, without any other reward, but the produce of one wheat corn for the fuft year, and that produce to be fowed from year to year, till the end of the time, allowing the increase but in a tenfold proportion? What is the fum of the whole produce! and, what will it amount to, at 5s per bufhel?

Anf

10

X10=10 I 1110 corns. Amount (56511. 8s. cod. 8. Suppofe one farthing had been put out at 61. per cent. per annum, compound intereft,† at the commence

ment

*Note, 7680 wheat or barley corns are fuppofed to make a pint.

Any fum, at 61. per cent per annum, compound interest will double in 11 years and thu ce hundred and twenty five days.or 11,839 years, or 11,89 is near enough; then if you divide 1784 by 11,89, it will give the number of terms in this cafe equal to 150 The ratio will be 2, and the first term 1.

ment of the Christian Era: what would it have amounted to in 1784 years; and fuppofe the amount to be in ftandard gold, allowing a cubick inch to be worth 53'. 2s. 8d. how large would the mafs have been?

2150 -I +1=148671634656874820943571455

Anf. 2-1

(15098907670653611. 11s. 32. 2798085972212123041597957123293359421076

(cubick inches of gold. As, 355 113: 360X69,5: 7964 Earth's diameter. 360 × 69,5 X 7964X1327,33= 264482820122 cubick miles in the globe = 67273337308854741368832000 inches in the globe. Then, 2798085972 21 21 2304159 79571232933594210766 67273337308854741368 832000=415930899840288,8 which however incredible it may appear to fome, is more than four hundred and 5fteen millions of millions, nine hundred and thirty thousand, eight hundred and ninety nine millions, eight hundred and forty thoufand, two hundred and eighty eight times larger than the globe we inhabit.

PROBLEM 3 The first term, the laft term, (or the extremes and the ratio given, to find the fum of the feries.

RULE. Divide the difference of the extremes by the ratio lefs by 1: Add the greater extreme to the quotient, and the refult will be the fum of all the terms.

Or, multiply the greatest term by the ratio, from the product fubtract the leaft term; then divide the remainder by the ratio, lefs by 1, and the quotient will be the fum of all the terms.

Or, when all the terms are given, then, from the product of the fecond and last terms fubtract the fquare of the firft term; this remainder being divided by the fecond term lefs the firft, will give the fum of the feries.

EXAMPLES.

1. If the feries be 2. 6. 18. 54. 162.486. 1458.

4374; What is its fum total ?

Firl

Divide by the ratio, lefs 13-1=2)4372 diff. ofex.

Divide by the ratio, lefs by 1X3-1=2)13120

Anf. 6560

4374X3-2

or,

-=6560

3

Multiply by the fecond term =

Subtract the fquare of the first term=2X2=

Div. the rem. by the 2d term lefs the 1ft-6-2=4)26240

།

Third Method.

Greateft term = 4374

4374

6

Product 26244

4

Anf. 6560

2. A man travelled 6 days; the first day he went 4 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 fons; to whom he be queathed his eftate as follows, viz to his youngelt fon 1oool.; to the eldest 50621. 10s. and ordered that each fon fhould exceed the next younger by the equal ratio of 1; What did the feveral legacies amount to? 5062,5-1000

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

PROB. 4. Given the extremes and ratio, to find the nume 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 fum will be the number of terms

*

Or, Subtract the logarithm of the leaft 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-greateft term.

3X 3X3X3X3X 3X3 Quo, 2187-7th power, then +18 the Aus.

Or,

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

PROB. 5 Given the leaft term, the ratio, and the fum of the feries, to find the laft term.

RULE.-Multiply the fum of the feries by the ratio, lefs; to that product add the firft term, and the refult divided by the ratio, will give the last term.

EXAMPLE.

If the ft term be 2, the ratio 3, and the sum of the feries 6560; What is the laft term?

3-1×6560+2

3.

-=4374 Anf.

SIMPLE INTEREST.

Intereft is a premium allowed by the borrower of any fum 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 intereft added together.
Intereft is of two forts, fimple and compound.

Simple intereft is that, which is allowed for the principal lent only

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

GENERAL