A pile of newspaper was 17 3/4 inches high. Each consecutive week for the next 5 weeks the height of pile increase by 8 7/12 inches. What is the height in inches, of the pile after 3 weeks?

Answer: the height in inches, of the pile after 3 weeks is 34 11/12 inches

Step-by-step explanation:

Each consecutive week for the next 5 weeks the height of pile increase by 8 7/12 inches. Converting 8 7/12 inches to improper fraction, it becomes 103/12 inches. The height is increasing in an arithmetic progression. The formula for determining the nth term of an arithmetic sequence is expressed as

Tn = a + (n - 1) d

Where

a represents the first term of the sequence.

d represents the common difference.

n represents the number of terms in the sequence.

From the information given,

a = 17 3/4 = 71/4 inches

d = 103/12 inches

n = 3 weeks

the height in inches, of the pile after 3 weeks, T3. Therefore,

T3 = 71/4 + (3 - 1) 103/12

T3 = 71/4 + 2 * 103/12 = 71/4 + 103/6

T3 = 419/12 inches = 34 11/12 inches