Question

There are 5 letters in the first row, 9 letters in the second row, and 13 letters in the third row on the whiteboard and so on. How many letters are there in 7th row?

a. 30
b. 29
c. 28
d. 27

Answer 1

To find the number of letters in the 7th row, we use the arithmetic sequence formula L_n = L_1 + (n-1)d. With L_1 being 5, n equal to 7, and the common difference d being 4, we calculate that there are 29 letters in the 7th row.

Step-by-step explanation:

To find out how many letters are in the 7th row on the whiteboard, we need to analyze the pattern given: there are 5 letters in the first row, 9 in the second, and 13 in the third, and so on. This indicates that each row has 4 more letters than the previous row. We can express this using an arithmetic sequence formula where the number of letters in the nth row is given by:

L_n = L_1 + (n-1)d

where:

• L_n is the number of letters in the nth row,
• L_1 is the number of letters in the first row,
• n is the row number, and
• d is the common difference between the rows.

Here, L_1 = 5 (number of letters in the first row), d = 4 (since each subsequent row has 4 more letters than the previous one), and n = 7 (since we want to find the number of letters in the seventh row).

Putting these values into the formula gives us:

L_7 = 5 + (7-1)4

L_7 = 5 + 24

L_7 = 29

Therefore, there are 29 letters in the 7th row on the whiteboard.