The nth term of a sequence is given by the formula n^3 + 11n . Find the first four terms of the sequence given by this formula and the first term of the sequence which is bigger than one million. Prove that all terms of the sequence are divisible by 6.
Three Four Five
Age 14 to 16 Challenge Level:
As shown in the diagram, two semi-circles (each of radius $1/2$)
touch each other, and a semi-circle of radius 1 touches both of
them. Find the radius of the circle which touches all three
semi-circles, and find a 3-4-5 triangle in the diagram.
The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the
NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to
embed rich mathematical tasks into everyday classroom practice.