Question

Enter a recursive rule for the geometric sequence. 10, −80, 640, −5120, ...

a(1)=
a(n)=

Answer 1

The recursive formula would be:

`a_1=10 \\a_(n)=a_(n-1) * (-8)`

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 2

The value is:

a(1)=10 and a(n)=(-8)×a(n-1)

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)