find the 11th term of the progression 27, 9, 3, ...
Looks like the pattern is dividing by 3:
27, 9, 3, 1, 1/3, 1/9, 1/27, 1/81, 1/243, 1/729, 1/2187
The 11th term would be 1/2187
To find the 11th term of the given arithmetic progression, we need to determine the common difference between the terms.
In this case, we can notice that each term is obtained by dividing the previous term by 3.
Starting with the first term 27:
Second term = 27 / 3 = 9
Third term = 9 / 3 = 3
So, it can be observed that the common difference is -18 (each term is obtained by subtracting 18 from the previous term).
Now, we can use the formula for the nth term of an arithmetic progression:
An = a1 + (n - 1)d
Where:
An is the nth term
a1 is the first term
d is the common difference
Substituting the values:
A11 = 27 + (11 - 1)(-18)
= 27 + (10)(-18)
= 27 - 180
= -153
Therefore, the 11th term of the given progression is -153.
To find the 11th term of the given progression, we first need to identify the pattern. In this case, we can see that each term is obtained by dividing the previous term by 3. Let's write out a few terms to confirm this pattern:
Term 1: 27
Term 2: 27 ÷ 3 = 9
Term 3: 9 ÷ 3 = 3
Now, we can continue this pattern to find the 11th term. Starting from the third term (3), we divide it by 3 to obtain the next term, and so on. Here are the next few terms:
Term 4: 3 ÷ 3 = 1
Term 5: 1 ÷ 3 = 1/3
Term 6: (1/3) ÷ 3 = 1/9
Continuing this pattern, we find:
Term 7: (1/9) ÷ 3 = 1/27
Term 8: (1/27) ÷ 3 = 1/81
Term 9: (1/81) ÷ 3 = 1/243
Term 10: (1/243) ÷ 3 = 1/729
Finally, we arrive at the 11th term of the progression:
Term 11: (1/729) ÷ 3 = 1/2187
Therefore, the 11th term of the given progression is 1/2187.