Question

Here are the first three terms of a different sequence 1, 2, 4, write down two numbers that can be the 4th and 5th terms of this sequence give the rule you have used to get your number.

Answer 1

Hey there! :)

Answer:

$n_{4} = 8\\ n_{5} = 16$

Formula: $f(n) = 2^{n-1}$

Step-by-step explanation:

Derive a rule from the numbers in the sequence:

$n_{1} = 1\\n_{2} = 2\\n_{3} = 4$

We can see that each number is double of the previous. We can write an explicit function describing this sequence:

$f(n) = 2^{n-1}$ where 'n' is the term number.

Substitute in to solve for the 4th and 5th terms:

$f(4) = 2^{4-1} = 2^{3} =8$

$f(5) = 2^{5-1} = 2^{4} =16$

Therefore:

$n_{4} = 8\\ n_{5} = 16$