The sum of the first $25$ terms of an arithmetic sequence is $1, 400$ , and the $25 t h$ term is $104$ . Find the value of $a_{2} - a_{1}$ where the first term of the sequence is $a_{1}$ and the second term is $a_{2}$ .

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Solution

The correct option is C $4$
The difference between first term and second term is common difference.
Let the common difference be $d$ and first term be $a$ .
$\Rightarrow a + 24 d = 104$ , $25 a + 25 \times 12 d = 1400$
$\Rightarrow a + 12 d = 56$ and $a + 24 d = 104$
$\Rightarrow 12 d = 48$
$\Rightarrow d = 4$

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