KA-0104Recursive rules
4 points, difficulty 2 of 3Level 5–6about 75sA sequence starts 1, 1, and every term after that is the sum of the two before it. What is the eighth term?
Hints
Take them one at a time. The first gives nothing away.
1A nudge
Write the terms in a numbered row.
2The strategy
Each term needs the two before it, so there is no shortcut. Write them across the page with their positions underneath, and read off the one you were asked for.
3The full solution
1, 1, 2, 3, 5, 8, 13, 21. The eighth term is 21.
Solution— no shortcut on this one
Generate the terms and number them: term 1 is 1, term 2 is 1, then 1 + 1 = 2, 1 + 2 = 3, 2 + 3 = 5, 3 + 5 = 8, 5 + 8 = 13, 8 + 13 = 21. The eighth term is 21. The transferable idea: write the position under every term - with two starting values it is very easy to be one out.
Why this is on the test: Two starting terms rather than one is exactly what makes students miscount the position, and this sequence appears in some form most years.