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Answer:

  • The sum of the series = 198.

Step-by-step 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,

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

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

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

  • The sum of the series = 198.

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Hope it helps!

[tex]\mathfrak{Lucazz}[/tex]

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