How many triangles?

 I took this lovely activity from Nolan Fossum's tweet. 

Zombie Puzzle

 

source: @PuzzleADayBlog

What Concepts Live Here?(Sample)

 

 

Sum of Consecutive Odd Numbers

 

Visual Proof

 What equation does the following image prove?

Problem 120: Arithmetic series

IBDP past paper question, taken from Revision Village.

Problem 117: Geometric Series Proof

Problem 113: Sums of Odd Numbers

Use the above figure only to find

1+3+5+7+....+49=?

Inspired by @Mathgarden

Problem 112: Sierpinski Triangles

What is the ratio of the black coloured triangles to the full triangle in the fourth iteration of the Sierpinski triangles?

Problem 111: Shaded Area

Imagine this pattern of triangles inside the big triangle goes infinity.

What is the ratio of the red area to the triangle's area?

(Source)

Problem 108: Arithmetic Series with Fractions

Problem 104: Arithmetic and Geometric Sequences

The general formulae for geometric and arithmetic sequences.

The 1st, 5th and 17th terms of an arithmetic sequence are the first three terms of a geometric sequence. Both sequences start from 8. 

Which term of the arithmetic sequence will be equal to the 4th term of the geometric sequence?