Question

WILL FAN AND MEDAL!!

Three terms of a geometric sequence are shown.

f(1) = 1, f(3) = 9, f(6) = –243

Which recursive formula could define the sequence?

A)f(n + 1) = 9f(n)
B) f(n + 1) = –9f(n)
C) f(n + 1) = 3f(n)
D) f(n + 1) = –3f(n)

Answer 1

how can we get from f(1) to f(3)?


that is 1 to 9


one possibility is that common ratio = 3

1 --> 1*3 --> 1*3*3

but the sixth term is negative so looks more like common ratio = -3

what do you think?

Answer 2

umm. i really dont know cause i just started on this topic and its a bit confusing

Answer 3

f(1) means the first function that is 1
f(3) = third = 9

f(n) means the value of the function when variable = n

f(n+1) means the value of the next one after n

so
f(n+1) = 3f(n)

means that for a function you get the next one by multiplying it by 3

in our case the number is -3

so which option is correct?

Answer 4

we can work out all the terms by multiplying by -3:-

1, -3, 9 , -27, 81, -243

that fits - the 6th term is -243

Answer 5

so its D then?

Answer 6

yes

Answer 7

oh ok, thanks for the help :)

Answer 8

yw