Question

Each row of *s has two more *s than the row immediately above it, as shown. Altogether, how many *s are contained in the first twenty rows?

a. 190
b. 210
c. 230
d. 250

Answer 1

To find the total number of *s in the first twenty rows, use the formula for the sum of an arithmetic sequence.

Step-by-step explanation:

To determine how many *s are contained in the first twenty rows, we need to find the total number of *s in each row and then sum them all up.

Given that each row has two more *s than the row immediately above it, we can notice that the number of *s in each row follows an arithmetic sequence. The first row has 1 *, the second row has 3 *, the third row has 5 *, and so on. We can express this pattern as an arithmetic sequence: 1, 3, 5, 7, 9, ...

The formula to find the sum of an arithmetic sequence is: Sum = (n/2) * (first term + last term). In this case, the first term is 1 and the last term is 1 + (n-1)*2, where n is the number of rows. Plugging in n = 20 into the formula, we get: Sum = (20/2) * (1 + (20-1)*2) = 10 * (1 + 19 * 2) = 10 * (1 + 38) = 10 * 39 = 390. Therefore, there are 390 *s contained in the first twenty rows.