Find $a_{30} - a_{20}$ for the $A P$ $: a, a + d, a + 2 d, a + 3 d, . . .$

60 d

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50 d

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10 d

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\frac{3}{2} d

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Solution

The correct option is D $10 d$
Here the first term is $a$ and the common difference is $d$ .
$n^{t h}$ term of the AP is given by,
$a_{n} = a + (n - 1) d$
$∴ a_{20} = a + 19 d$ ... $(1)$
$a_{30} = a + 29 d$ ... $(2)$
On subtracting $(1)$ from $(2)$ , we get
$a_{30} - a_{20} = 10 d$

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