tower of blocks 10 rows high. there are 19 blocks in the bottom row. 17 blocks in the second, and so on .. how many blocks in the entire tower
2006-10-31 01:59:51 · 5 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
There are 100 blocks in your tower.
19 + 17 + 15 + ... + 1 = 100
or
(number of rows)^2 = 100
2006-10-31 02:05:37 · answer #1 · answered by bromothymol 4 · 0⤊ 1⤋
The tower is 10 rows high. With each row, 2 blocks decrease. The total number of blocks is:
19+17+15+13+11+9+7+5+3+1 = 100 blocks
2006-10-31 02:10:23 · answer #2 · answered by Akilesh - Internet Undertaker 7 · 0⤊ 1⤋
№ of Blocks = 19 + 17 + 15 + ..... + 5 + 3 + 1
№ of Blocks = 1 + 3 + 5 + ..... + 15 + 17 + 19
Add these together
2 X № of Blocks = 20 + 20 + 20 + .... + 20 + 20 + 20
= 10 X 20
= 200
So № of Blocks = 100
Alternate solution
1 + 3 = 4 = 2²
1 + 3 + 5 = 9 = 3²
1 + 3 + 5 + 7 = 16 = 4²
So 1 + 3 + 5 + 7 + .... + 19 = ??² = ???
2006-10-31 02:14:24 · answer #3 · answered by Wal C 6 · 0⤊ 0⤋
19 + 17 + 15 ... + 1.
Add the first and last numbers and you get 19+1=20.
Add the second and second-last numbers, 17+3=20.
etc.
2006-10-31 02:05:56 · answer #4 · answered by Anonymous · 0⤊ 1⤋
sum of n odd natural numbers=n^2
so the no of blocks=10^2=100
2006-10-31 02:11:04 · answer #5 · answered by raj 7 · 0⤊ 0⤋