Very Average

If each number in this list is the average of the two numbers before it, what is the value of a?
Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving
Being curious Being resourceful Being resilient Being collaborative

Problem



In the list below, each number (from $b$ onwards) is the mean of the two numbers before it.

$40$, $a$, $b$, $c$, $d$, $150$


Find the value of $a$