The third term of a geometric progression is 63/4 and the sixth term is 1701/32. Find the sum of the first 12 terms of the sequence.

The sum of the first 12 terms of the sequence is 2703.673096

Step-by-step explanation:

The nth term of a geometric progression is a(n) = , where

The sum of n terms of the geometric progression is s(n) =

∵ The third term of a geometric progression is

∴ a(3) =

∵ a(3) = ar²

→ Equate its two right sides

∴ ar² =  ⇒ (1)

∵ The sixth term is

∴ a(6) =

∵ a(6) = a

→ Equate its two right sides

∴ a =  ⇒ (2)

→ Divide (2) by (1)

∴ r³ =

→ Take ∛  for both sides

∴ r = = 1.5

→ Substitute the value of r in (1) to find a

∵ a(1.5) =

∴ 1.5a = 15.75

→ Divide both sides by 1.5

∴ a = 10.5

→ Let us find the sum of the first 12 terms

∵ n = 12, a = 10.5, and r = 1.5

→ Substitute them in the rule of the sum above

∵ s(12) =

∴ s(12) = 2703.673096

∴ The sum of the first 12 terms of the sequence is 2703.673096

a.) list the factors of 40.

1/2/4/5/8/10/20/40

b.) list the factors of 40 that represent the number of cans that could be on each shelf.

5

c.) how many different arrangements of cans are possible?

just one because if you put more on one shelf you will go way over 40 and the cabinet will probably break.

d.) what are the possible arrangements of the cans?

put 5 cans on each self to reach 40 cans in total.

e.) which arrangement uses all the shelves?

5 because you can put 5 cans on each shelf, and since there are 8 shelfs you are equally going to get 40 cans.