Respuesta :
The recursive formula would be:
[tex]a_1=10 \\a_{n}=a_{n-1} \times (-8)[/tex]
This is because the first term, a₁, is 10. A recursive rule is dependent upon the term before it (a(n-1)) and the common ratio. The common ratio, or the number that each term is multiplied by, is -8.
[tex]a_1=10 \\a_{n}=a_{n-1} \times (-8)[/tex]
This is because the first term, a₁, is 10. A recursive rule is dependent upon the term before it (a(n-1)) and the common ratio. The common ratio, or the number that each term is multiplied by, is -8.
Answer:
The value is:
a(1)=10 and a(n)=(-8)×a(n-1)
Step-by-step explanation:
We are given a sequence as:
10, -80 , 640 , -5120 ,.........
since by looking at the sequence we could see that it is a geometric progression (G.P.) with common ratio -8.
Also a(1) denotes the first term of the sequence and a(n) denotes the nth term of the sequence.
a(1)=10
Also a(n)=(-8)×a(n-1)
since a(1)=10
a(2)=(-8)×10=-80
a(3)=(-8)×(-80)=640
a(4)=(-8)×640=-5120
and so on.
Hence the answer is:
a(1)=10 and a(n)=(-8)×a(n-1)
