What is the nth term of the progression 27, 9, 3,...
The common ratio between consecutive terms is 1/3. Therefore, the nth term of this progression can be written as:
27 * (1/3)^(n-1)
So, for example:
- The 4th term would be 27 * (1/3)^(4-1) = 27 * (1/27) = 1
- The 6th term would be 27 * (1/3)^(6-1) = 27 * (1/243) = 0.111...
To find the nth term of a progression, we need to first figure out the pattern or rule behind the given numbers.
Looking at the given numbers, we can see that each number is obtained by dividing the previous term by 3.
Starting with 27, we can find the next terms by dividing each term by 3:
27 ÷ 3 = 9
9 ÷ 3 = 3
So, the pattern or rule for this progression is that each term is obtained by dividing the previous term by 3.
To find the nth term, we can express this rule using mathematical notation:
aₙ = aₙ₋₁ ÷ 3
where aₙ represents the nth term and aₙ₋₁ represents the (n-1)th term.
Using this rule, we can find the nth term.