Give the next 3 numbers in the sequence and verbally explain the pattern like say what number am I adding by, subtracting by, multiplying by, or dividing by. Please help ASAP this question is due by tomorrow!!! :(
1/2, 2/3, 3/4, 4/5,...
doesn't look too hard.
Consider the numerators as a sequence.
Then consider the denominators...
where A is the value of a term , and n is the number of the term (1st, 2nd, etc)
An = n / (n + 1)
it is a pattern ... no mathematical operation involved
To find the pattern in the given sequence, let's examine the changes between each term.
In the given sequence, we observe that each term is formed by adding 1 to the numerator (top number) and adding 1 to the denominator (bottom number) of the previous fraction.
For example:
1/2 → Numerator +1 = 1 + 1 = 2, Denominator +1 = 2 + 1 = 3 → 2/3
2/3 → Numerator +1 = 2 + 1 = 3, Denominator +1 = 3 + 1 = 4 → 3/4
3/4 → Numerator +1 = 3 + 1 = 4, Denominator +1 = 4 + 1 = 5 → 4/5
Based on this pattern, we can continue the sequence as follows:
4/5 → Numerator +1 = 4 + 1 = 5, Denominator +1 = 5 + 1 = 6 → 5/6
5/6 → Numerator +1 = 5 + 1 = 6, Denominator +1 = 6 + 1 = 7 → 6/7
6/7 → Numerator +1 = 6 + 1 = 7, Denominator +1 = 7 + 1 = 8 → 7/8
So, the next three numbers in the sequence are 5/6, 6/7, and 7/8.