Question

A tile pattern has 10 tiles in Figure 2 and increases by 2 tiles for each figure. Find a rule for this pattern then determine how many tiles are in Figure 100. Pls help. =_=

Answer 1

The rule for the pattern of tile increase is T(n) = 8 + (n-1)*2, where n is the figure number. By applying this rule, Figure 100 has 206 tiles.

Step-by-step explanation:

A rule for a tile pattern where the number of tiles increases by a constant amount for each subsequent figure. Given that there are 10 tiles in Figure 2, and it increases by 2 tiles for each next figure, we can deduce that each figure number corresponds to a certain number of tiles by following a linear pattern. The rule for the pattern is to start with 8 tiles for Figure 1 (since Figure 2 has 10, and we're adding 2 for each next figure), and add 2 tiles for every next figure number. To express this as a formula, we can use the formula for a linear sequence: T(n) = a + (n-1)d, where T(n) is the number of tiles in Figure n, a is the first term (number of tiles in Figure 1), n is the figure number, and d is the common difference (the number of tiles we're adding each time, which in this case is 2).

Using the formula:

• a (first term) = 8 tiles (start with this many for Figure 1)
• d (common difference) = 2 tiles (because each figure have 2 more tiles than the previous one)

So the formula to find the number of tiles in Figure n is:

T(n) = 8 + (n-1)×2

To find the number of tiles in Figure 100, plug 100 in place of n:

T(100) = 8 + (100-1)×2

T(100) = 8 + 198 = 206 tiles

Therefore, Figure 100 has 206 tiles.

Answer 2

Basically the pattern is the figure number multiplied by two plus 6. For example, 2 x 2 is 4. 4 + 6 is 10. Now for 100: 100 times 2 is 200, plus 6 is 206.