Find recursive and explicit formula for -40 -36 -32 -28
Tn = -44+4n
T1 = -40
Tn = T(n-1)+4
As an after-thought .....
Tn = T(n-1) + 4 , T1 = -40 , n > 1
In the recursive notation, the initial value has to be included or else you can't begin your sequence.
To find the recursive and explicit formulas for the given sequence -40, -36, -32, -28, you first need to observe the pattern in the sequence.
When examining the sequence, you'll notice that each term is four units greater than the previous term. Therefore, the common difference (d) between consecutive terms is +4.
Now, let's define the first term as a_1 = -40. To find the next term, we can apply the recursive formula which relates each term with its previous term.
Recursive Formula:
a_n = a_(n-1) + d
In this case, where a_1 = -40 and d = 4:
a_2 = a_1 + d = -40 + 4 = -36
a_3 = a_2 + d = -36 + 4 = -32
a_4 = a_3 + d = -32 + 4 = -28
Therefore, the recursive formula for the given sequence is:
a_n = a_(n-1) + 4
Now let's move on to finding the explicit formula for the sequence.
Explicit Formula:
a_n = a_1 + (n-1) * d
In this case, where a_1 = -40 and d = 4:
a_n = -40 + (n-1) * 4
Thus, the explicit formula for the given sequence is:
a_n = -40 + 4n - 4
a_n = -44 + 4n