The first, second and last terms of an A.P. are $a, b$ and $2 a$ respectively. Then, the number of terms in the A.P. is

\frac{b}{b - a}

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\frac{b}{b + a}

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\frac{a}{b - a}

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\frac{a}{a + b}

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Solution

The correct option is A $\frac{b}{b - a}$
Let $A$ an $D$ be the first term and common difference of the given AP respectively. Let there be $n$ terms in this AP.
Given, $A = a, t_{2} = b a n d l a s t t e r m = t_{n} = 2 a$
$\Rightarrow A + D = b \Rightarrow D = b - a$
$A l s o, A + (n - 1) D = 2 a$
$\Rightarrow a + (n - 1) \times (b - a) = 2 a$ ( $∵ D = b - a$ )
$\Rightarrow (n - 1) \times (b - a) = a \Rightarrow n - 1 = \frac{a}{b - a}$
$\Rightarrow n = \frac{a}{b - a} + 1 = \frac{b}{b - a}$
Hence, Option A is correct

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