The required explicit formula is
<h3><u>Solution:</u></h3>
Given that sequence is -4, 12, -36, 108
<em><u>To find: explicit formula</u></em>
Explicit formulas define each term in a sequence directly, allowing one to calculate any term in the sequence
An explicit formula designates the nth term of the sequence, as an expression of n (where n = the term's location). It defines the sequence as a formula in terms of n.
<em><u>Let us first find the logic used in sequence</u></em>
So we can see clearly that next term in sequence is obtained by multiplying -3 with previous term
This can be defined in terms of "n"
Where represents the next terms location and represents previous term location
So the required explicit formula is
<em><u>Let us verify our explicit formula</u></em>
Now let us find the 4th term of sequence
Thus using the explicit formula, next terms in sequence can be found