Enter a recursive rule for the geometric sequence. 10, −80, 640, −5120,  a(1)= a(n)=

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)

1/4 and 8/3 because:

the reciprocal if 4 is 1/4 because 4 is used as 4/1 and the opposite of that is 1/4. the opposite of 3/8 is 8/3 so that is the answer.