If $A_{1}, A_{2}, A_{3}, . . ., A_{n}$ are $n$ arithmetic means between $a$ and $b$ . Find the common difference between the terms.

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Solution

Let common difference be $d$ .

Here, first term $= a$ , total number of terms $= (n + 2)$

${(n + 2)}^{t h}$ term $= b$

$\Rightarrow b = a + (n + 2 - 1) d$

$\Rightarrow b - a = (n + 1) d$

$\Rightarrow d = \frac{b - a}{n + 1}$

Thus, the common difference between the terms is $\frac{b - a}{n + 1}$

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