Fibonacci deduction
Leonard writes down a sequence of numbers. Can you find a formula to predict the seventh number in his sequence?
Age
11 to 14
Challenge level
Problem
Leonard writes down a sequence of numbers. After the first two numbers, each number is the sum of the previous two numbers in the sequence. The fourth number is $6$ and the sixth number is $15$. What is the seventh number in the sequence?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
Student Solutions
_ , _ , _ , 6 , _ , 15
Let the fifth number be $x$:
_ , _ , _ , 6 , $x$ , 15
The sixth number is $6+x= 15$, so $x=9$.
_ , _ , _ , 6 , 9 , 15
The seventh number is the sum of the fifth and sixth numbers, $9+15=24$:
_ , _ , _ , 6 , 9 , 15 , 24