Question

Write an explicit rule for each geometric sequence using subscribe notation. Use the calculator and around your answer to the nearest 10th if necessary. The numbers of teams remaining in each round of a single illumination tennis tournament represent a geometric sequence were a(n) Is the number of teams competing and in is the round. There are 32 teams remaining around four and 8 teams in round six

Answer 1

a = 256; r =
`$ (1)/(2)  $`

Explanation:

The general form of the geometric sequence is:

a, ar, ar², ar³, . . .

where 'a' is the first term of the sequence;

'r' is the common difference.

Fourth term of the sequence = ar³ = 32

Sixth term of the sequence = ar⁵ = 8

Dividing both the equations, we get:

`$ (ar^5)/(ar^3) = (8)/(32) $`

⇒ r² =
`$ (1)/(4) $`

⇒ r =
`$ (1)/(2) $`

Therefore, we get a = 32 X 8

a = 256

The first term of the sequence is 256 and the common difference is
`$ (1)/(2) $`.

Hence, the answer.