Question

The third term of geometric sequence is 63/ 4 , and the sixth term is 1701 /32 find the fifth term

Answer 1

`(567)/(16)`

Explanation:

A geometric sequence is one where

`A_1 = b\\A_2 = ba\\A_3 = ba^2\\A_4 = ba^3\\A_5 = ba^4\\`

and so on, so forth

So,

`A_3 = ba^2 = (63)/(4)\\\\A_6 = ba^5 = (1701)/(32)\\\\(A_6)/(A_3) = (ba^5)/(ba^2) = a^3 = (1701)/(32)/(63)/(4) = (1701\cdot 4)/(32 \cdot 63) = (27)/(8)\\\\a^3 = (27)/(8)\\\\a = (3)/(2)\\\\A_6 = A_5 \cdot a\\\\A_5 = (A_6)/(a) = (1701)/(32) / (3)/(2) = (567)/(16)`