Question

Determine the common ratio and find the next three terms of the geometric sequence.

9,3/3, 3

Answer 1

Answer:D

Explanation:

Answer 2

The common ratio is
`(√(3) )/(3)` and the next three terms of the sequence are
`√(3), 1, (1)/(√(3) )`

Explanation:

Given the geometric series a1, a2, a3... the common ratio is expressed as;

r = a2/a1 = a3/a2

The nth term of a geometric sequence Tn =
`ar^(n-1)`

where n is the number of terms

r is the common ratio

Now given the sequence 9,3
`√(3)`, 3...

common ratio
`r=(3√(3) )/(9) = (3)/(3√(3) ) = (√(3) )/(3)`

The next three terms are the 4th, 5th and 6th term

To get the 4th term when n = 4

`=9*((√(3) )/(3)) ^(4-1)\\=9*((√(3) )/(3)) ^(3)\\\\= 9*(√(27) )/(27)\\= (3√(3) )/(3)\\ T4 = √(3) \\`

When n= 5

`T5 =9*((√(3) )/(3)) ^(5-1)\\T5=9*((√(3) )/(3)) ^(4)\\= 9*(√(81) )/(81)\\ T5= (81)/(81) \\T5 = 1`

when n = 6

`=9*((√(3) )/(3)) ^(6-1)\\=9*((√(3) )/(3)) ^(5)\\\\= 9*(√(243) )/(243)\\ = 9*(9√(3) )/(243) \\= (81√(3) )/(243) \\= (√(3) )/(3) \\T6 = (1)/(√(3) )`

The next three terms of the sequence are
`√(3), 1, (1)/(√(3) )`