Pattern Pastori is planning to build a staircase and is unsu

Pattern Pastori is planning to build a staircase and is unsure how many steps high he wants his stairs. He knows that a one-step stair takes one black to build, a two-step stair takes three blocks, and a three-step staircase takes six blocks. How many blocks will a ten-step staircase use?

Generalize a pattern to this type of staircase construction so that Mr.Pastoriwill be able to find the number of blocks needed in any step staircase he may want to build.

Solution

Step ---- No.Of Blocks

1 ----- 1

2 ------ 3

3 -------- 6

Further we can extend the pattern:

4 -------- 10

5 --------- 15

6 ---------- 21

7 ---------- 28

8 ---------- 36

9 ---------- 45

10 ---------- 55 (blocks)

Lets find a Generalised pattern to find the nu. of blocks

= (number of steps) x (number of steps +1))/2

= (2x 3)/2 =3

= (10*11)/2 = 55

So, rule works