Question

You visit the Grand Canyon and drop a penny off the edge of a cliff. The distance of 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 is the total distance the object will fall in 6 seconds?

Answer 1

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Answer 2

• The total distance the object will fall in 6 seconds is equal to 576 feet .

Given :-

• The distance of the penny will fall in first second = 16 feet
• The distance of the penny will fall in second second = 48 feet
• The distance of the penny will fall in third second = 80 feet

To Find :-

• The total distance the object will fall in 6 seconds ?

Concept / Formula used :-

• A sequence is said to be in AP (Arithmetic Progression), if the difference between its consecutive terms are equal.

• The nth term of an AP is given as :-

• T(n) = a + (n-1)•d , where a is the first term and d is the common difference.

• The common difference of an AP is given as :-

• d = T(n) - T(n-1)

• The sum up to nth terms of an AP is given as :-

• S(n) = (n/2)[2a + (n - 1)d]

Solution :-

since the given sequence is in AP, we have,

→ First term (a1) = 16 feet

→ Second term (a2) = 48 feet

So,

→ Common difference (d) = a2 - a1 = 48 - 16 = 32 feet .

then,

→ Sum of nth term of AP (Sn) = (n/2)[2a + (n - 1)d]

As we have to find the total distance the object will fall in 6 seconds . We can conclude that, we need to find S(6) .

therefore,

→ S(n) = (n/2)[2a + (n - 1)d]

→ S(6) = (6/2)[2•16 + (6 - 1)•32]

→ S(6) = 3[32 + 5 × 32]

→ S(6) = 3[32 + 160]

→ S(6) = 3 × 192

→ S(6) = 576 feet (Ans.)

Hence, the total distance the object will fall in 6 seconds is equal to 576 feet .

Learn more :-

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