Respuesta :
[tex]T_{n}[/tex] = 6 - n is the explicit formula for the sequence.
What is an arithmatic sequence?
A sequence of numbers which increases or decreases by a constant amount each term is called an arithmatic sequence.
- That common amount (term) is called common difference, which can be calculated by subtracting a term from its next term.
How to find the explicit formula for the given sequence?
The given sequence is 5,4,3,2,1.
- This is an arithmatic sequence with common difference -1.
We can find the explicit formula by finding the nth term of this series.
- We know that for an arithmatic sequence, we can find the nth term from the formula,
[tex]T_{n} = a+(n-1)d[/tex]
Where,
[tex]T_{n}[/tex] is the nth term of the arithmatic sequence,
a is the first term of the arithmatic sequence,
d is the common difference
Comparing with the given sequence,
a = 5
d = -1
∴[tex]T_{n}[/tex] = 5 + (n -1)(-1)
= 6 - n
So, the explicit formula is [tex]T_{n}[/tex] = 6 - n
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