Find a general term a Subscript n for the sequence, whose first four terms are given. 4,6,8,10
an = 2 n + 2
To find the general term, a Subscript n, for the sequence where the first four terms are given as 4, 6, 8, and 10, we need to identify the pattern or rule that governs how each term is generated.
By observing the given sequence, we can see that each term is obtained by adding 2 to the previous term. Let's check the differences between consecutive terms to confirm this:
6 - 4 = 2
8 - 6 = 2
10 - 8 = 2
As we can see, the differences are all equal to 2. This suggests that the general term is found by adding 2 to the previous term.
Now, let's express this relationship using mathematical notation:
a Subscript n = a Subscript (n-1) + 2
In this equation, a Subscript n represents the general term we are looking for, and a Subscript (n-1) represents the previous term.
Therefore, the general term for the given sequence is:
a Subscript n = a Subscript (n-1) + 2
Using this general term, we can find any term in the sequence by substituting the value of n. For example, if we want to find the 10th term, we would substitute n = 10 into the formula:
a Subscript 10 = a Subscript (10-1) + 2
a Subscript 10 = a Subscript 9 + 2
To find the value of a Subscript 9, we can apply the same rule:
a Subscript 9 = a Subscript (9-1) + 2
a Subscript 9 = a Subscript 8 + 2
Continuing this process, we eventually reach the first term, which is given as 4. From there, we can work backward to find any term in the sequence.