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in Arithmetic Progression by (22.8k points)
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If the first, second, and last terms of an arithmetic series are a, b and c respectively, then what is the number of terms?

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Best answer

Last term = c 

Let the number of terms be n. Then 

c = a + (n – 1) × d ⇒ c = a + (n – 1) × (b – a) 

⇒ c – a = (n – 1) (b – a)

⇒ (n - 1) = \(\frac{c-a}{b-a}\)

⇒ n = \(\frac{c-a}{b-a}\) + 1 

\(\frac{c-a +b -a}{b-a}\) = \(\frac{c + b - 2a}{b-a}\)

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