Question

You visit the Grand Canyon and drop a penny off the edge of a cliff. The distance the penny will fall is 16 feet the first second, 48 feet the next second, 80 feet the third second, and so on in an arithmetic sequence. What distance will the penny fall in the sixth second?

Answer 1

The penny falls according to an arithmetic sequence with a common difference of 32 feet. Using the formula for the nth term of an arithmetic sequence, the penny will fall 176 feet in the sixth second.

Step-by-step explanation:

To solve for the distance the penny will fall in the sixth second, we must first determine the common difference in the arithmetic sequence provided. The sequence starts at 16 feet for the first second, increases to 48 feet by the second second, and further to 80 feet by the third second.

• First Second: 16 feet
• Second Second: 48 feet - The increase is 32 feet (48 - 16)
• Third Second: 80 feet - The increase is again 32 feet (80 - 48)
  

We can see that the common difference (d) is 32 feet. Each second, the distance the penny falls will increase by 32 feet compared to the previous second. To find the distance it will fall in the sixth second, we need to use the formula for the nth term of an arithmetic sequence:

dn = d1 + (n - 1) × d

Here, d1 is the first term, which is 16 feet, and d is the common difference:

d6 = 16 + (6 - 1) × 32

d6 = 16 + 5 × 32

d6 = 16 + 160

d6 = 176 feet

Thus, the penny will fall 176 feet in the sixth second.

Answer 2

Step-by-step explanation:

The distance the penny will fall is 16 feet the first second, 48 feet the next second, 80 feet the third second, and so on in an arithmetic sequence. The formula for the nth term of an arithmetic sequence is expressed as

Tn = a + (n-1)d

Where

a represents the first term of the sequence.

n represents the number of terms

d represents the common difference.

From the information given,

a = 16

d = 48 - 16 = 80 - 48 =32

n = 6

T6 represents the sixth term of the sequence. Therefore

T6 = 16 + (6-1)32

T6 = 16 + 160

T6 = 176