How do you find #S_n# for the geometric series #a_1=343#, #a_n=-1#, r=-1/7? Precalculus Series Sums of Geometric Sequences 1 Answer Binayaka C. · Jumbotron Jul 10, 2017 #S_n = 300# Explanation: #a_1=343 , a_n= = -1 , r= -1/7# Given that #a_n = "last term"# #a_1 = "first term"# #r = -1/7# #T_n = a_1 cdot r^(n-1)# Recall that #T_n = a_n# Hence #-># #a_n = a_1 cdot r^(n-1)# #a_n= a_1*r^(n-1) or 343 * (-1/7)^(n-1) = -1 or (-1/7)^(n-1) = -1/343 # or #(-1/7)^(n-1) = (-1/7)^3 :. n-1 = 3 or n =4 # #S_n = a_1 * ( r^n -1)/(r-1) = 343 * ((-1/7)^4-1 ) /(-1/7-1)# # =343*(1/2401-1)/(-8/7) = 343 * (-2400/2401)* (-7/8) # #= cancel343* 300/cancel343 =300# #S_n = 300# [Ans] Answer link Related questions What is a sample problem about finding the sum of a geometric sequence? What is the formula for the sum of a geometric sequence? What is a sample problem about finding the sum of a geometric sequence? How do I find the sum of the geometric sequence #3/2#, #3/8#? What is the sum of the geometric sequence 3, 15, 75? What is the sum of the geometric sequence 8, 16, 32? How do I find the sum of the geometric series 8 + 4 + 2 + 1? How do you find the sum of the following infinite geometric series, if it exists. 2 + 1.5 +... How do you find the sum of the first 5 terms of the geometric series: 4+ 16 + 64…? How do you find S20 for the geometric series 4 + 12 + 36 + 108 + …? See all questions in Sums of Geometric Sequences Impact of this question 2119 views around the world You can reuse this answer Creative Commons License