Mathematics · Class 10

Arithmetic Progression

An arithmetic progression is a sequence where the difference between consecutive terms is constant. This pattern appears frequently in real life and i

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What is the difference between an AP and a geometric progression?

In an AP, consecutive terms have a constant difference. In a geometric progression, consecutive terms have a constant ratio. AP: 2, 5, 8, 11 (add 3 each time). GP: 2, 6, 18, 54 (multiply by 3 each time).

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Can the common difference be negative or zero?

Yes, the common difference d can be any real number. If d is negative, the AP is decreasing. If d equals 0, all terms are the same constant value. If d is positive, the AP is increasing.

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How is the sum formula derived?

Write the sum forward and backward, then add them: S equals a plus (a + d) plus ... plus l. S equals l plus (l minus d) plus ... plus a. Adding gives 2S equals n(a plus l), so S equals n(a plus l) divided by 2, where l is the last term.

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