Question

Please help meee oh please

Answer 1

Collecting the data of this P.G., comes:

The 1st term
`a_(1) = 648`
The 2nd term
`a_(2) = 216`

The ratio
`r = \frac {a2}{a1}`
The number of terms n = 8

The 8th term
`a_(8) = ?`

The value of ratio, we have:
The ratio
`r = \frac {a2}{a1}`

`r = \frac {a2}{a1} = (216)/(648) (/6)/(/6) = (36)/(108) (/6)/(/6) = (6)/(18) (/6)/(/6) \to\:r= (1)/(3)`

Applying the general term formula of P.G., comes:

`a_(n) = a_(1) *r^(n-1)`

`a_(8) = 648 * ((1)/(3)) ^(8-1)`

`a_(8) = 648 * ((1)/(3)) ^(7)`

`a_(8) = 648 * (1)/(3^7)`

`a_(8) = 648 * (1)/(2187)`

`a_(8) = (648)/(2187)`
Simplify


`a_(8) = (648)/(2187) (/9)/(/9) = (72)/(243) (/9)/(/9) \to\: \boxed{\boxed{a_(8) = (8)/(27)}}\end{array}}\qquad\quad\checkmark`

Answer:

`\boxed{\boxed{a_(8) = (8)/(27)}}`