Find the nth term of a sequence whose first several terms are given.
3, 5, 3, 5, 3, 5, . . .
an =
For this sequence, we can see that the terms 3 and 5 are repeating. Since the sequence consists of alternating terms, we can represent it as follows:
3, 5, 3, 5, 3, 5, . . .
Looking at the pattern, we can see that the first term is 3, and the second term is 5. So, we can say that the first two terms are:
a1 = 3
a2 = 5
Now, we need to find a pattern for the remaining terms. It is clear that the sequence alternates between 3 and 5. So, we can express it more generally as:
an = 3 if n is odd
an = 5 if n is even
In other words, if n is an odd number, the term will be 3, and if n is an even number, the term will be 5.
Therefore, the nth term of the sequence can be written as follows:
an = 3 if n is odd
an = 5 if n is even
To find the nth term of the given sequence, let's analyze the pattern:
The sequence alternates between the numbers 3 and 5. We can see that the first term (n = 1) is 3, and the second term (n = 2) is 5. From observation, we can see that the pattern repeats itself with every two terms.
So, we can conclude that the sequence can be represented by the following formula:
an = 3 + 2((n-1) mod 2)
Using this formula, we can find the nth term of the sequence.