The sum of third and ninth term of an A.P is $8$ . Find the sum of the first $11$ terms of the progression

44

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22

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19

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None of the above

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Solution

The correct option is A $44$
The third term $t_{3} = a + 3 d$
The ninth term $t_{9} = a + 8 d$
$t_{3} + t_{9} = 2 a + 10 d = 8$
Sum of first $11$ terms of an AP is given by
$S_{11} = \frac{11}{2} [2 a + 10 d]$
$S_{11} = \frac{11}{2} \times 8 = 44$

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