Competition problem — Algebra — Maths Olympiad Prep

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Algebra Difficulty 1.8 Junior Find the answer

The first four terms of a sequence are $1,4,2$ , and 3. Beginning with the fifth term in the sequence, each term is the sum of the previous four terms. What is the eighth term?

Your answer

A number or a short expression. Spacing and $ signs are ignored.

Solution

The first four terms of the sequence are $1,4,2,3$ . Since each term starting with the fifth is the sum of the previous four terms, then the fifth term is $1+4+2+3=10$ . Also, the sixth term is $4+2+3+10=19$ , the seventh term is $2+3+10+19=34$ , and the eighth term is $3+10+19+34=66$ .

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