Thus, the sum of the 4th powers sx sum of the cubes sum of the squares.

The sum of the 5th powers sx sum of the 4th sum of the cubes.

рого

The sum of the 6th powers sx sum of the 5th p sum of the 4th powers, &c. &c.

Hence the sum of the nth powers of x and y will?

iven the first term 5, the last term 41, and the sum of series 299, to find the number of terms, and the common ference? Ans. by theor. 8. n=13, and by theor. 19. d=3. 6. Given the first term 4, the common difference 7, and the sum 355, to find the last term, and number of terms? Ans. by theor. 17. z=67, and by theor. 12. n=10.

The last term is 67, the difference 7, and the number of

ROGR Mbers in

we have x=√35.25+.5, whence 1+6=√/35.25 +6.5: the numbers 7,and 12.43717, nearly.

ork as many days at 3 shillings per his pocket; at the end of the time d spent nothing, he finds himself n did he begin with?

illings at first, whence also x=the e have therefore here given the first 3, and the number of terms x+1,

to find the last term; now by 11=x+x+1−1x3, that is, 4x= sum he began with.

in arithmetical progression, such,
the sum of their squares 56?
nce, 3s=(12) the sum, then will
he less extreme, and s+x=the
then by the problem, (s—x)2+
ance 2x2-a-3s2, and x=
fres=4,s-x=2, and s+x=6,
rs required.

thmetical progression, whereof
?, and that of the means 70?
e common difference; then will
sent the progression. Let a=
x.x+3y=) x2+3xy=a, and
; from the latter equation sub-

whence y = √ 20
b-a

-=3; sub

terms 10, being given, to find the first term and sum by theor. 15. s=355.

8. Let the common difference 3, the number o and the sum 299 be given, to find the first and 5, and by theor. 13. z=41.

9. Let the last term 67, the number of terms sum 355, be given, to find the first term and diff by theor. 6. a4, and by theor. 14. d=7.

term be 9, the difference 1, an first term, and number of terms?

18. a=2, and by theor. 16. n=8.

term 0, the last term 15, an
given, to determine the diff
d=3, and by theor. 24. s=4
100 rabbits, and gave for the fi
did they cost?
Ans. 81. 6s. 8d.
earned 3d. the first day, 8

on, till on the last day he c.
Ans. 12 days.

S equidifferent numbers, tl
What are the numbers?

Paid 1000l. at 12 equidiffere.

was the second, and the Last 1661. 13s. 4d.

cleared 50l. the first year

cleared regularly every year 51. more than he gain in the last year, and w