How do you find the sum of the arithmetic sequence 100 + 95 + 90 + ... 5?

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Answer 1 · 2016-08-18T18:36:41

Just to clarify what the other contributor said...

Step 1: Determine the number of terms

We determine the number of terms using the formula $t_{n} = a + (n - 1) d$ $t_n = a+ (n - 1)d$ :

$5 = 100 + (n - 1) - 5$ $5 = 100 + (n - 1)-5$

$5 = 100 - 5 n + 5$ $5 = 100 - 5n + 5$

$5 n = 100 + 5 - 5$ $5n = 100 + 5 - 5$

$5 n = 100$ $5n = 100$

$n = 20$ $n = 20$

Step 2: Find the sum

We are now able to find the sum using the formula $s_{n} = \frac{n}{2} (a + t_{n})$ $s_n = n/2(a + t_n)$

$s_{20} = \frac{20}{2} (100 + 5)$ $s_20 = 20/2(100 + 5)$

$s_{20} = 10 (105)$ $s_20 = 10(105)$

$s_{20} = 1050$ $s_20 = 1050$

Hence, the sum of the arithmetic sequence is $1050$ $1050$ .

Hopefully this helps!