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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