Write the expression $a_{n} - a_{k}$ for the $A . P . a, a + b, a + 2 d, . . . .$ . Hence find the common difference of the $A . P .$ for which
$a_{10} - a_{5} = 200$

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Solution

$a_{n} = a + (n - 1) d$

$a_{10} - a_{5}$

$= a + 9 d - a - 4 d$

$= 5 d$

$∴ 200 = 5 d$

$\Rightarrow d = 40$

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Write the expression an−ak for the A.P. a, a+b, a+2d,..... Hence find the common difference of the A.P. for which a10−a5=200

an=a+(n−1)da10−a5=a+9d−a−4d=5d∴200=5d⇒d=40

Write the expression $a_{n} - a_{k}$ for the $A . P . a, a + b, a + 2 d, . . . .$ . Hence find the common difference of the $A . P .$ for which
$a_{10} - a_{5} = 200$

$a_{n} = a + (n - 1) d$

$a_{10} - a_{5}$

$= a + 9 d - a - 4 d$

$= 5 d$

$∴ 200 = 5 d$

$\Rightarrow d = 40$