For the sequence, write an explicit formula for the nth term.
1/5, 2/7, 3/9, 4/11...
I don't know how to start. I have other sequences also, so I need to learn, not just get the answer. Thank You
top is just 1,2,3,4, ...n
top = n
bottom would be 2 n but have to start with 5 when n = 1 and 2n=2 so
bottom = (3+2n)
so
An = n/(3+2n)
To find an explicit formula for this sequence, it's helpful to first observe the pattern.
We can see that the numerators (1, 2, 3, 4) are increasing by 1 with each term, while the denominators (5, 7, 9, 11) are increasing by 2 with each term.
To represent this pattern mathematically, we can express the nth numerator as n, and the nth denominator as 2n + 3.
So, the explicit formula for the nth term of the sequence is:
aₙ = n / (2n + 3)
Now you can use this formula to find any term in the sequence by plugging in the value of n.
To find an explicit formula for the nth term of a sequence, we need to look for a pattern in the sequence. In this case, we have the sequence:
1/5, 2/7, 3/9, 4/11...
To understand the pattern, let's break it down:
The numerator starts at 1 and increases by 1 with each term (1, 2, 3, 4...). This suggests that the numerator can be represented by the variable n, indicating the position of the term.
The denominator starts at 5 and increases by 2 with each term (5, 7, 9, 11...). This suggests that the denominator can be represented by the expression 2n + 3.
Therefore, the pattern can be represented by the formula:
𝑛/(2𝑛 + 3)
This is the explicit formula for the nth term of the given sequence. To find any term in the sequence, substitute the appropriate value of n into the formula.