Question

Find the average of the multiples of 3 between 1 and 100​

Answer 1

Step-by-step explanation:

therefore the average multiples of 3 between 1 to are 34

Answer 2

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To Find:

• Average of multiples of 3 between 1 and 100

Solution:

$:\implies Average= \dfrac{\text{Sum of all values}}{\text{Total Values}} = \dfrac{S_n}{n} \\\\:\implies \text{Sum of all multiples of 3 between 1 and 100} \\\\:\implies \text{1st multiple of 3 = 3, last multiple = 99} \\:\implies a=3, d = 3, l=99, n => \\\\:\implies l = a + (n-1)d => 99 = 3 + (n-1)3 => 96 = 3(n-1)\\\\:\implies n-1 = 32 => n = 33.\\\\:\implies S_n = \dfrac{n}{2} (a+l) => \dfrac{33}{2}(3+99)=>\dfrac{33}{2}*102 \\\\:\implies S_n = 33*51 => 1683.\\\\\bf{:\implies Average = \dfrac{S_n}{n} => \dfrac{1683}{33} => 51}$

Hope it helps!!!!