SOLUTION: The 4th term of a sequence is 4 and the 6th term is 6. Every term of the sequence is the sum of the two preceding terms. Find the 2nd term.

Question 252039: The 4th term of a sequence is 4 and the 6th term is 6. Every term of the sequence
is the sum of the two preceding terms. Find the 2nd term.
Answer by RicaMath(8) (Show Source): You can put this solution on YOUR website!
Let's write out what we know of the sequence so far, and use letters as variables for the items that we don't know. Since the problem states that the 4th term of the sequence if 4, and the 6th term of the sequence is 6, we have this:

A, B, C, 4, D, 6

Now, we are trying to find the 2nd term, which is currently labeled B.

We know that every term of the sequence is the sum of the two preceding terms. So, in this case, let's take the 6. The two preceding terms are 4 and D, so:

4 + D = 6
D = 2

Now our sequence looks like:

A, B, C, 4, 2, 6

Let's keep working backwards until we get to the item we are looking for, B. Let's take the 2 we just found. The two preceding terms are 4 and C, so:

4 + C = 2
C = -2

Now our sequence looks like:

A, B, -2, 4, 2, 6

Let's take the 4. The two preceding terms are -2 and B, so:

-2 + B = 4
B = 6

As mentioned earlier, we were looking for the 2nd term, which we labeled B. Therefore, the 2nd term in this sequence is 6.
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