Insert a series of numbers between two numbers $$a$$ and $$b$$, such that the new sequence which has $$ n+2$$ terms, is an arithmetic sequence, then the common difference of the sequence is

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Uniteasy Admin · Accepted Answer

Let q be the common difference of the arithmetic sequence
$$a_1 = a$$
$$a_n = a_1+(n-1)q$$
$$a_{n+2} = a+(n+1)q = b $$
$$q = \dfrac{b-a}{n+1}  $$

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