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Mathematics

The mean of numbers in A.P. 2, 4, 6, 8, ……, 40 is :

  1. 40+22\dfrac{40 + 2}{2}

  2. 202(2+40)\dfrac{20}{2}(2 + 40)

  3. 102\dfrac{10}{2} (2 + 40)

  4. 840

Statistics

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Answer

Given,

A.P. : 2, 4, 6, 8, ……, 40

a = 2, d = 2.

In an A.P.,

⇒ an = a + (n - 1)d

⇒ 40 = 2 + 2(n - 1)

⇒ 40 - 2 = 2(n - 1)

⇒ 38 = 2(n - 1)

⇒ n - 1 = 382\dfrac{38}{2}

⇒ n - 1 = 19

⇒ n = 19 + 1

⇒ n = 20.

Sum of A.P. = n2(a+l)=202(2+40)\dfrac{n}{2}(a + l) = \dfrac{20}{2}(2 + 40).

Hence, Option 2 is the correct option.

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