Answer:
The explicit formula is [tex]a_{n}[/tex] = - 13 - 7n
Step-by-step explanation:
Let us at first find the type of the sequence
∵ The terms are - 20, - 27, - 34, - 41, ............
→ Find the difference between each to consecutive terms
∵ - 27 - (- 20) = - 27 + 20 = - 7
∵ - 34 - (- 27) = - 34 + 27 = - 7
∵ - 41 - (- 34) = - 41 + 34 = - 7
→ There is a constant difference between each two consecutive terms
∴ The sequence is Arithmetic
→ The explicit formula of the nth term of the arithmetic sequence is
- [tex]a_{n}=a+(n-1)d[/tex], where
- a is the first term
- d is the constant difference
- n is the position of the number
∵ a = - 20
∵ d = -7
∴ [tex]a_{n}=-20+(n-1)(-7)[/tex]
→ Simplify it
∴ [tex]a_{n}[/tex] = - 20 + (-7)(n) - (-7)(1)
∴ [tex]a_{n}[/tex] = - 20 + (-7n) - (-7)
∴ [tex]a_{n}[/tex] = - 20 - 7n + 7
→ Add the like terms
∴ [tex]a_{n}[/tex] = (- 20 + 7) - 7n
∴ [tex]a_{n}[/tex] = - 13 - 7n
The explicit formula is [tex]a_{n}[/tex] = - 13 - 7n
