A. -x^3 and x^11 ; 3

Question

B. 0.6 and -0.002025; 2
C. x^2,x^6,x^10.... (A sub 20) * sorry for the sub :D but I guess that's already clear? Hehe.
D. a^2/2 , a^4/4, a^6/8.... (A sub 10)
E. X+1, 2x^2 + 2x, 4x^3 + 4x^2 (A sub 6)
F. 32y^2, 16y^2, 8y^2 (A sub 8)

* sorry for the sub thingy guys. I just can't find another way to explain it. Hehe :D

Problems:
I. The cells in a culture divide every hour. Write a formula for the number of cells in the culture at the end of "n" hours. If there are 200 cells now, how many cells will there be at the end of 5 hours?
II. A piece of spoiled meat has some bacteria in it. The amount of bacteria increases four times every hour. If the amount of bacteria is 1500 on the 1st hour what's the total amount of bacteria at the end of 6 hours?
III. Three number of forms a geometric sequence and their sum is 70. If the smallest and the largest numbers are each multiplied by 4 and the middle number is multiplied by 5, the resulting products from an arithmetic sequence. Find the numbers.

I really need help. This is just hard for me :D and really big thanks to bobpursley ;) for answering the problem a while ago.

Answer 1

no idea what A and B are supposed to mean

You need to recognize powers of 2 and simple multiples

C: An = x^(4n-2)
D: An = x^(2n)/2^n
E: An = 2^n(x^n + x^(n-1))
F: An = 64y^2/2^n

I: 200*2^n
II: 375*4^n
III: If the numbers are x,y,z then we have

y/x = z/y
x+y+z = 70
5y-4x = 4z-5y

GP: 10,20,40
AP: 40,100,160
or the reverse works, as well

Answer 2

I. is 200 *2^n
if n = 5, then 200 * 32

II. 2^4 = 16 times as much every hour if it doubles every quarter hour 1500*16^6
(infinite :)

III. a r^n + a r^n+1 + a r^n+2 = 70
or
a r^2 (1 + r + r^2) = 70

4 a r^n + 5 a r^n+1 + 4 a r^n+2 is arithmetic
so
5a r^n+1 - 4a r^n = d
4a r^n+2 - 5a r^n+1 = d
or
5ar -4a = 4ar-5a
ar = -9 a
r = -9 etc