Question

The first three towers in a sequence are shown. The tower is formed by stacking $n$ blocks on top of an $n \times n$ square of blocks. How many blocks are in the 99th tower?
[asy] pair A;
for(int i = 1; i<4; ++i){
A = ((i-1)*(i+4)/2,0);
for(int k = 0; k <= i; ++k){
draw(A+(k,0)--A+(k,i)); draw(A+(0,k)--A+(i,k));
draw(A+(i-1,i+k)--A+(i,i+k));
}
draw(A+(i-1,i)--A+(i-1,2*i));draw(A+(i,i)--A+(i,2*i));
}
label("1", (1-1/2,0),S);
label("2", 5/2 + (2-1/2,0),S);
label("3", 6 + (3-1/2,0),S);
[/asy]

Answer 1

Answer:

970,398 blocks

Step-by-step explanation:

the formula that can be derived from the statement given in question could be written as;

Let say that we want to see how many block are there in nth tower

Number of block in nth tower = n + (n x n^2)

Now for the 99th tower,

Number of blocks in 99th tower = 99 + ( 99 x 99^2)

Number of blocks in 99th tower = 970,398