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

the correct answer is a) "catholic church".

the proposals that liberals in mexico made during 1855 were particularly focused on a person's individual rights, such as the freedom of speech, the freedom of conscience, freedom of assembly, and the right to possess weapons.

when the constitution was formally published 2 years later (1857). it also contained an article which permitted education free from any religious influence, the removal of the catholic church institutional privileges, and the sale of property belonging to the church. all of these provisions were clearly against the catholic church interests.