why is the common difference between 31 and 87 is 2 ?
The statement that the common difference between 31 and 87 is 2 is incorrect.
To find the common difference between two numbers in an arithmetic sequence, you subtract the first number from the second number, which gives you the difference in their values. In this case, the difference between 31 and 87 is 87 - 31 = 56, not 2.
Therefore, the common difference between 31 and 87 is 56.
The common difference between two terms in a sequence is the constant value by which each term increases or decreases.
To determine the common difference between 31 and 87, we subtract the first term from the second term:
87 - 31 = 56.
However, the common difference in this case is not 2, but rather 56.
To determine why the common difference between 31 and 87 is 2, we need to understand the concept of an arithmetic sequence.
An arithmetic sequence is a sequence of numbers in which the difference between any two consecutive terms is constant. This constant difference is called the common difference.
In the given sequence, the first term is 31 (let's call it "a1") and the second term is 87 (let's call it "a2"). We want to figure out the common difference.
To find the common difference, we can use the formula for the nth term of an arithmetic sequence:
an = a1 + (n-1)d
where:
an is the nth term of the sequence,
a1 is the first term,
n is the position of the term in the sequence, and
d is the common difference.
Let's plug in the values we have:
a1 = 31
a2 = 87
n = 2
We want to solve for d. Substituting the given values into the formula, we have:
a2 = a1 + (2-1)d
87 = 31 + d
Now, let's rearrange the equation to solve for d:
d = 87 - 31
d = 56
So, the common difference between 31 and 87 is 56, not 2. It seems there may be a mistake in the original question or calculation.