Question

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

Answer 1

• 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.

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Hope it helps!

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