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.
4/9, 4/27, 4/81, 4/243.
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
To find the next terms in the sequence 36, 12, 4, 4/3..., we can notice a pattern where each term is divided by 3 to get the next term.
Let's break down the pattern step by step:
First term: 36
To find the second term, we divide the first term by 3: 36 ÷ 3 = 12
Second term: 12
To find the third term, we divide the second term by 3: 12 ÷ 3 = 4
Third term: 4
To find the fourth term, we divide the third term by 3: 4 ÷ 3 = 4/3
Fourth term: 4/3
To find the fifth term, we divide the fourth term by 3: (4/3) ÷ 3 = 4/9
Fifth term: 4/9
To find the sixth term, we divide the fifth term by 3: (4/9) ÷ 3 = 4/27
Sixth term: 4/27
To find the seventh term, we divide the sixth term by 3: (4/27) ÷ 3 = 4/81
Seventh term: 4/81
To find the eighth term, we divide the seventh term by 3: (4/81) ÷ 3 = 4/243
Continuing this pattern of dividing the previous term by 3, we can find the next four terms:
Eighth term: 4/243
Ninth term: (4/243) ÷ 3 = 4/729
Tenth term: 4/729
Eleventh term: (4/729) ÷ 3 = 4/2187
Twelfth term: 4/2187
Thirteenth term: (4/2187) ÷ 3 = 4/6561
Therefore, the next four terms are 4/243, 4/729, 4/2187, and 4/6561.