pattern is made up of black and white tiles. it is 7 tiles across .In the City Hall there is a pattern like this which is 149 tiles across. How many tiles all together? Please show work and how you got it.
Consider the tiles in the pattern above, but not including the 149 tile row. That row contains 147 tiles. The next higher row contains 145 tiles and the number decreases by 2 for each successive row. The number of tiles above the 149 tile row is the sum of the odd integers from 1 to 147. N = 1 + 3 + 5 + 7 + ... + 145 + 147 N = Σ(2n-1) for n = 1 to 74 = 2Σn - Σ1 = 2(n)(n+1)/2 - n = 2(74)(75/2) - 74 = 74*75 - 74 = 74? tiles The pattern is symmetric about the 149 tile row so there are the same number of tiles below that row as there are above it. Including the 149 tile row the total number of tiles is: T = 2N + 149 = 2(74?) + 149 = 11101
