Question

For each sequence, write the next four terms
1. 36,12,4,4/3...
I know that the pattern in that the term is divided by 3, but I have no idea how to calculate/write the next four terms.

Answer 1

4/9, 4/27, 4/81, 4/243.

Answer 2

an = 4 * 3 ^ ( 3 - n )



For n = 1

a1 = 4 * 3 ^ ( 3 - 1 ) = 4 * 3 ^ 2 = 4 * 9 = 36


For n = 2

a2 = 4 * 3 ^ ( 3 - 2 ) = 4 * 3 ^ 1 = 4 * 3 = 12


For n = 3

a3 = 4 * 3 ^ ( 3 - 3 ) = 4 * 3 ^ 0 = 4 * 1 = 4


For n = 4

a4 = 4 * 3 ^ ( 3 - 4 ) = 4 * 3 ^ ( - 1 ) = 4 / 3 ^ 1 = 4 / 3


For n = 5

a5 = 4 * 3 ^ ( 3 - 5 ) = 4 * 3 ^ ( - 2 ) = 4 / 3 ^ 2 = 4 / 9


For n = 6

a6 = 4 * 3 ^ ( 3 - 6 ) = 4 * 3 ^ ( - 3 ) = 4 / 3 ^ 3 = 4 / 27


For n = 7

a7 = 4 * 3 ^ ( 3 - 7 ) = 4 * 3 ^ ( - 4 ) = 4 / 3 ^ 4 = 4 / 81


For n = 8

a7 = 4 * 3 ^ ( 3 - 8 ) = 4 * 3 ^ ( - 5 ) = 4 / 3 ^ 5 = 4 / 243