Mathematics

Mathematics

Problem

An athlete runs 2 km on the first day of training and increases the distance by 0.25 km each day. Calculate the total distance he will have run in the first 20 days. a) 90 km90\,\text{km} b) 85 km85\,\text{km} c) 87.5 km87.5\,\text{km} d) 80 km80\,\text{km}
Intuitive explanation

This is an arithmetic sequence problem where you're adding up terms that follow a predictable pattern. The key insight is recognizing that the daily distances form a sequence with a constant difference (d=0.25d = 0.25 km), so you can use the arithmetic series formula rather than adding all 20 distances individually. You'll need to find the 20th term first, then apply the sum formula to get your total.

Intuitive explanation

This is an arithmetic sequence problem where you're adding up terms that follow a predictable pattern. The key insight is recognizing that the daily distances form a sequence with a constant difference (d=0.25d = 0.25 km), so you can use the arithmetic series formula rather than adding all 20 distances individually. You'll need to find the 20th term first, then apply the sum formula to get your total.

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