The first and seventh terms of a sequence are both 8. Starting with the third term, each term is the sum of the two previous terms. What is the fifth term?
The sequence is
8 -4 4 0 4 4 8
5th term 4
To find the fifth term of the sequence, we need to first understand the rule that is given for generating the sequence. The rule states that each term in the sequence, starting from the third term, is the sum of the two previous terms.
Let's write down the given information:
First term (a1) = 8
Seventh term (a7) = 8
Now, we need to find the common difference between consecutive terms to apply the rule. To do that, we can subtract the first term from the seventh term.
a7 - a1 = 8 - 8 = 0
Since the difference is zero, it means that the common difference between consecutive terms is zero. In other words, all the terms in the sequence are the same.
Since the first term is given as 8, we can conclude that all the terms of the sequence are equal to 8.
Now, we need to find the fifth term. Since all the terms are 8, the fifth term is also 8.
Therefore, the fifth term of the sequence is 8.