Respuesta :
Answer:
see explanation
Step-by-step explanation:
(a)
given the sequence
- 2, - 6 , - 10 , ........
there is a common difference between consecutive terms
- 6 - (- 2) = - 6 + 2 = - 4
- 10 - (- 6) = - 10 + 6 = - 4
This indicates the sequence is arithmetic with nth term
[tex]a_{n}[/tex] = a₁ + d(n - 1)
a₁ is the first term, d the common difference, n the term number
here a₁ = - 2 , d = - 4 , then
[tex]a_{n}[/tex] = - 2 - 4(n - 1) = - 2 - 4n + 4 = - 4n + 2
To find the 25th term, substitute n = 25 into [tex]a_{n}[/tex]
a₂₅ = - 4(25) + 2 = - 100 + 2 = - 98
(b)
given the sequence
27, - 9 , 3
there is a common ratio between consecutive terms
[tex]\frac{-9}{27}[/tex] = - [tex]\frac{1}{3}[/tex]
[tex]\frac{3}{-9}[/tex] = - [tex]\frac{1}{3}[/tex]
This indicates the sequence is geometric with nth term
[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]
a₁ is the first term, r the common ratio, n the term number
here a₁ = 27 , r = - [tex]\frac{1}{3}[/tex] , then
[tex]a_{n}[/tex] = 27[tex](-\frac{1}{3}) ^{n-1}[/tex]
To find the 8th term, substitute n = 8 into [tex]a_{n}[/tex]
a₈ = 27 [tex](-\frac{1}{3}) ^{7}[/tex] = 27 × - [tex]\frac{1}{2187}[/tex] = - [tex]\frac{27}{2187}[/tex] = - [tex]\frac{1}{81}[/tex]
