Question

Given the sequence 4, -16, 64, -256..a) Write the explicit rule for the sequence. b) Find a7 c) Write the recursive rule for the sequence.

Answer 1

the given series is 4 -16 64 -256

that is

4 x -4 = -16 = -4^2

-16 x -4 = 64 = 4^3

64 x -4 = -256 = -4^4

so we can say that is every time the number is multiplied with -4,

for a7, as 7 is an odd number so the negative sign will be there from the above observations

-4^7 = -16384

the recursive rule will be'

`a_n=a_(n-1)*-4`