1. ## 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)

2. 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 $180 - \left(90 + \frac{x}{2}\right) = 90 - \frac{x}{2}$

remaining base angle is $180 - \left[x + \left(90 - \frac{x}{2}\right)\right]$

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 $\frac{n(n+1)}{2}$ ... so, (n+1)st term is formed by replacing n with n+1 ... $\frac{(n+1)[(n+1)+1]}{2}$

simplify the last expression.