First slide

Means - A.M/G.M/H.M

Question

$If a_{1}, a_{2}, a_{3}, \dots \dots \dots, a_{20} are A.M's between 13 and 67, then the value of$ $a_{1} + a_{2} + a_{3} + \dots \dots + a_{20} is equal to$

Moderate

A

600
B

800
C

400
D

200

Solution

$∵ a_{1}, a_{2}, a_{3}, \dots \dots \dots, a_{20} are A.M's between 13 and 67, then$ $13, a_{1}, a_{2}, \dots \dots ., a_{20}, 67 are in A.P.$
$We know that if a_{1}, a_{2}, a_{3}, \dots \dots \dots, a_{n} are \underset{}{\underset{}{A} \cdot M^{'}} s between a and b,$
$a_{1} + a_{2} + a_{3} + \dots \dots \dots . . + a_{n} = n (\frac{a + b}{2}) then$
$∴ a_{1} + a_{2} + a_{3} + \dots \dots \dots . . + a_{20} = 20 (\frac{13 + 67}{2}) = 800$

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