Find the sum of arithmetic sequence Sum of integers between 6 and 30 ??

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Answer 1 · 2018-06-25T20:24:26

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Here you are solving $30 \sum r = 6 r$ $sum_(r=6) ^30 r$

$30 \sum r = 6 r = 30 \sum r = 1 r - 5 \sum r = 1 r$ $sum_(r=6) ^30 r = sum_(r=1) ^30 r - sum_(r=1) ^5 r$

Use:

$n \sum r = 1 r = \frac{n}{2} (n + 1)$ $sum_(r=1) ^n r = n/2 (n+1)$

$= \frac{30}{2} (30 + 1) - \frac{5}{2} (5 + 1)$ $= 30/2(30+1) - 5/2(5+1)$

$= 450$ $= 450$

from 6 to 30, inclusive is 450

from 6 to 30, exclusive is $450 - 6 - 30 = 414$ $450 - 6 - 30 = 414$