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#:

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

#5 = 100 - 5n + 5#

#5n = 100 + 5 - 5#

#5n = 100#

#n = 20#

Step 2: Find the sum

We are now able to find the sum using the formula #s_n = n/2(a + t_n)#

#s_20 = 20/2(100 + 5)#

#s_20 = 10(105)#

#s_20 = 1050#

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

Hopefully this helps!