If a 1 , a 2 , a 3 , … , a 20 are in A.P. and a 1 + a 20 = 45 , then a 1 + a 2 + a 3 + ? + a 20 is equal to

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Solution

Q.
If $a_{1}, a_{2}, a_{3}, \dots, a_{20}$ are in A.P. and $a_{1} + a_{20} = 45$ , then $a_{1} + a_{2} + a_{3} + \dots + a_{20}$ is equal to _________.

Ans.
(450)

$S_{n} = \frac{n}{2} (a + l)$

$∴$ $S_{20} = \frac{20}{2} (45) = 450$ $(∵ a_{1} + a_{20} = 45)$

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