How do you find the number of terms n given the sum #s_n=366# of the series #3+8+13+18+23+...#?

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Answer 1 · 2016-09-04T15:27:52

There are #12# terms.

Use the formula #s_n = n/2(2a + (n - 1)d)#, solving for #n#.

#366 = n/2(2(3) + (n - 1)5)#

#366 = n/2(6 + 5n - 5)#

#366 = n/2(1 + 5n)#

#366 = n/2 + (5n^2)/2#

#366 xx 2 = 5n^2 + n#

#732 = 5n^2 + n#

#0 =5n^2 + n - 732#

#0 = 5n^2 - 60n + 61n - 732#

#0 = 5n(n - 12) + 61(n - 12)#

#0 = (5n + 61)(n - 12)#

#n = -61/5 and 12#

Hopefully this helps!