How do you find the number of terms given #s_n=820# and #1+9+81+729+...#?

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Answer 1 · 2016-08-23T02:10:04

#n = 4#

We use the formula #s_n = (a(1 - r^n))/(1 - r)# to find the sum of any geometric series.

In our case, #r = 9#, #a = 1# and #s_n = 820#. We are looking for #n#.

#820 = (1(1 - 9^n))/(1 - 9)#

#820(-8) = 1 - 9^n#

#-6560 - 1 = -9^n#

#-6561 = -9^n#

#6561 = 9^n#

#9^4 = 9^n#

#n = 4#

Hence, there are #4# terms in this series.