Given the Recursive Formula:
a1 = −8
a6 = an +5
What is the common difference?
To find the common difference, we need to find the value of a2, which is the next term after a1 in the sequence.
Since a1 = -8 and a2 = a1 + 5, we can substitute the value of a1 into the equation:
a2 = -8 + 5
= -3
Therefore, the common difference is 3.
To find the common difference in a recursive sequence, we need to find the difference between consecutive terms.
In this given recursive formula, let's find the difference between a6 and a5, and a5 and a4.
Given: a6 = an + 5
To find a5, we substitute n = 6 - 1 = 5 into the formula:
a5 = a5-1 + 5
Since a5-1 is a4, we can write it as:
a5 = a4 + 5
Similarly, we can find that:
a4 = a3 + 5
Therefore, we have a sequence of equations:
a5 = a4 + 5
a4 = a3 + 5
Now, let's substitute these equations into each other to eliminate a4:
a5 = (a3 + 5) + 5
Simplifying:
a5 = a3 + 10
So, the difference between a5 and a3 is 10.
Therefore, the common difference in this sequence is 10.
To find the common difference, we need to first determine the difference between consecutive terms in the sequence.
Using the recursive formula a1 = -8 and a6 = an + 5, we can find the difference between a6 and a1.
Let's substitute the values into the formula:
a6 = an + 5
a6 = a1 + 5
Substituting the values, we have:
-8 + 5 = a1 + 5
-3 = a1
The difference between a6 and a1 is -3. Therefore, the common difference is -3.