How do you find the number of terms n given the sum #s_n=375# of the series #-10+(-5)+0+5+10+...#?

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Answer 1 · 2016-08-26T14:44:59

There are #15# terms in this series.

We use the formula #s_n = n/2(2a + (n -1)d)# to find the sum of an arithmetic series.

Here, #a = -10#, #d = 5#, #s_n = 375# and #n = ?#

We will thus be solving for n.

#375 = n/2(2(-10) + (n - 1)5)#

#375 = n/2(-20 + 5n - 5)#

#375 = -25/2n + 5/2n^2#

#750 = 5n^2 - 25n#

#0 = 5n^2 - 25n - 750#

#0 = 5(n^2 - 5n - 150)#

#0 = (n - 15)(n + 10)#

#n = 15 or -10#

A negative answer is impossible, so there are #15# terms in this series.

Hopefully this helps!