Question

Let 1st pattern has 1 tiles, 2nd pattern has 4 tiles, 3rd pattern has 9 tiles, 4th pattern has 16 tiles. How many total tiles will be from 1st to 11th tiles? Tell the formula also to find the result.

Answer 1

The total number of tiles from the first to the 11th pattern is 1012. The formula to find the sum of the squares of numbers from 1 to n is (n)(n + 1)(2n + 1)/6.

Step-by-step explanation:

The pattern in this sequence is that the number of tiles in each pattern is the square of the pattern number. So, for the first pattern, the number of tiles is 1^2 = 1. For the second pattern, the number of tiles is 2^2 = 4. And so on. To find the total number of tiles from the first to the 11th pattern, we can find the sum of the squares of the numbers from 1 to 11. The formula for this is:

Sum = (n)(n + 1)(2n + 1)/6

Plugging in n = 11, we get:

Sum = (11)(11 + 1)(2(11) + 1)/6 = 11(12)(23)/6 = 11(4)(23) = 1012