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A frog fell into a drain that was 245 inches deep. For every jump, the frog climbs 7 inches, but slides down 4 inches. If this pattern continues, how many hops will it take the frog to get out of the drain?

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Answer:

81 jumps

Explanation:

You want the number of jumps required to escape from a drain 245 inches deep if each jump climbs 7 inches, but slides back 4.

Sequence

The heights in inches reached after 1, 2, 3 jumps are ...

7, 10, 13, ...

That is, the n-th jump will reach a height of 3n+4 inches.

Escape

To obtain a height of 245 inches, we require ...

3n +4 ≥ 245

3n ≥ 241

n ≥ 80 1/3 . . . . . . . where n is an integer

It will take 81 hops for the frog to escape the drain.

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Additional comment

On the 80th jump, the frog reaches a height of 244 inches, but slides back to 240. The 81st jump will take the frog to a height of 247 inches, which gets it out of the drain.

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