Fibonacci deduction

Leonard writes down a sequence of numbers. Can you find a formula to predict the seventh number in his sequence?

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.