f(n)=1/2n−13 as an arithmetic fraction
3 answers
f(n) = 1/(2n) - 13
f(n)=1/2n−13 as an arithmetic sequence
To represent the expression 1/2n - 13 as an arithmetic sequence, we need to find the general form of the sequence.
The general form of an arithmetic sequence is given by the formula a_n = a_1 + (n-1)d, where a_n is the nth term, a_1 is the first term, n is the position of the term in the sequence, and d is the common difference.
In the expression 1/2n - 13, the term 1/2n represents the first term. This means that a_1 = 1/2n.
Then, we have to find the common difference. To do this, we can rewrite the given expression as f(n) = 1/(2n) - 26/2. This allows us to see that the common difference is -26/2 = -13.
Therefore, the general form of the arithmetic sequence is a_n = 1/(2n) + (n-1)(-13).
The general form of an arithmetic sequence is given by the formula a_n = a_1 + (n-1)d, where a_n is the nth term, a_1 is the first term, n is the position of the term in the sequence, and d is the common difference.
In the expression 1/2n - 13, the term 1/2n represents the first term. This means that a_1 = 1/2n.
Then, we have to find the common difference. To do this, we can rewrite the given expression as f(n) = 1/(2n) - 26/2. This allows us to see that the common difference is -26/2 = -13.
Therefore, the general form of the arithmetic sequence is a_n = 1/(2n) + (n-1)(-13).