Thread: Explain/ Triangular Sequence

Can anybody help me with these two questions:

1. Given a triangle with the 'base' at the bottom, single angle at the top. The base line is extended to the right. The exterior angle is 90 + (x/2). The top angle is x. How do I prove that it is isosceles?

2. Explain why the (n+1)th term of a triangular sequence is given by
1/2(n+1)(n+2) given that the nth term is 1/2n(n+1)

1. Given a triangle with the 'base' at the bottom, single angle at the top. The base line is extended to the right. The exterior angle is 90 + (x/2). The top angle is x. How do I prove that it is isosceles?

interior angle adjacent to the given exterior angle is

remaining base angle is

simplify this expression and see what you get.

2. Explain why the (n+1)th term of a triangular sequence is given by 1/2(n+1)(n+2) given that the nth term is 1/2n(n+1)

nth term is ... so, (n+1)st term is formed by replacing n with n+1 ...

simplify the last expression.