Figure 3 of a tile pattern has 11 tiles, while Figure 4 has 13 tiles. The pattern grows at a constant rate

tile-pattern

#1

Figure 3 of a tile pattern has 11 tiles, while Figure 4 has 13 tiles. The pattern grows at a constant rate. a. Write an equation to represent this situation b. Which figure number will contain 1015 tiles?

Answer:

Fig.3 contains 11 Tiles
Fig.4 contains 13 Tiles
At a Contstant Rate, Continuing like this we get
Fig.(n+2) contains an amount of tiles equivalent to n th term of the sequence of numbers 11,13,15,17,_ _ _ _ _ _ ,which is in Arithematic Progression having first term a=11 and Common Difference d=2.
n th Term of Sequence = a+(n-1)d =11+(n-1)2 = 2n+9
Now 2n+9 =1015
2n=1006
n=503
Therefore n+2=503+2=505 figure contains 1015 Tiles

The Equation representing this Problem would be
"Figure K contains 2(K-2)+9 = 2K+5 Tiles."