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13. 6 + 10 + 14 + ... + 38
Find the sum of the arithmetic series

User Linqu
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7 votes

Answer:

  • The sum of the series = 198.

Explanation:

In the given arithmetic series,

  • The first term (a) = 6
  • Common difference (d) = (aₙ – aₙ₋₁) = 10 - 6 = 4
  • Last term (aₙ) = 38

To find the sum of the series, we need to find the number of terms (n) at first. So,


a_(n) = a + (n - 1)d\\38 = 6 + (n - 1) 4\\38 - 6 = 4n - 4\\32 = 4n - 4\\32 + 4 = 4n\\36 = 4n\\36 / 4 = n\\\boxed{9 = n}

Now, let's find the sum of the arithmetic series (Sₙ).


S_(n) = (n)/(2) [2a + (n - 1)d]\\S_(n) = (9)/(2) [2*6 + (9 -1)4]\\S_(n) = (9)/(2) [12+ (8*4)]\\S_(n) = (9)/(2) [12+ 32]\\S_(n) = (9)/(2) (44)\\S_(n) = 9*22\\\boxed{S_(n) = 198}

  • The sum of the series = 198.

_______________

Hope it helps!


\mathfrak{Lucazz}

User Mooncake
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