Question

Bernardo and Ogechi were asked to find an explicit formula for the sequence 1\,,\,8\,,\,64\,,\,512,...1,8,64,512,...1, comma, 8, comma, 64, comma, 512, comma, point, point, point.

Bernardo said the formula is h(n)=1\cdot8^{\large{n}}h(n)=1⋅8

n

h, left parenthesis, n, right parenthesis, equals, 1, dot, 8, start superscript, n, end superscript, and

Ogechi said the formula is h(n)=8\cdot1^{\large{n}}h(n)=8⋅1

n

h, left parenthesis, n, right parenthesis, equals, 8, dot, 1, start superscript, n, end superscript.

Which one of them is right?

Answer 1

none

Explanation:

Answer 2

`h_(n)=1.(8)^(n-1)` will be the correct formula for the given sequence.

Explanation:

The given sequence is 1, 8, 64, 512...........

The given sequence is a geometric sequence having a common ratio (r) of

r =
`\frac{\text{Second term}}{\text{First term}}`

r =
`(8)/(1)=8`

Since explicit formula of a geometric sequence is given by

`T_(n)=a(r)^(n-1)`

where
`T_(n)` = nth term of the sequence

a = first term of the sequence

r = common ratio of the successive term to the previous term

Now we plug values of a and r in the formula to get the explicit formula for the given sequence.

`T_(n)=1.(8)^(n-1)`

Therefore, if Bernardo is saying that the formula of the sequence is

h(n) =
`1.(8)^(n-1)` then he is correct.