The sum of the first 20 terms of an AP is known to be 1280, and the common difference is 20. Then the fourth term of the AP will be __.

-64

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-66

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-62

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-60

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Solution

The correct option is B
-66

Given, the sum of first 20 terms is 1280.
Let the first term be $a$ ,
and the common difference be $d$
$d = 20$ (given)

$\Rightarrow S_{20} = \frac{20}{2} (2 a + (20 - 1) 20) = 1280$
$\Rightarrow 10 (2 a + 19 (20)) = 1280$
Now, from the above equation
we can calculate the value of $a$ ,
We get $a = - 126$ .
Fourth term = $a_{4}$
$a_{4} = a + (4 - 1) d$
$= - 126 + (4 - 1) 20$
$= - 126 + 60 = - 66.$

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