Calculate the sum of the series 4 + 12 + 36 + ... + 2916. Please can you help?

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Answer 1 · 2018-07-08T19:02:20

The sum of the series : 4+12+36+...+2916=4372

Here,

#4,12,36,...,2916to "geometric sequence"#

Where, #a_1=4 and "common ratio r="12/4=36/12=3 #

#color(red)(n^(th) "term of geometric sequence is : "#

#a_n=a_1*(r)^(n-1)=2916#

#=>4*(3)^(n-1)=2916#

#=>(3)^(n-1)=2916/4#

#=>(3)^(n-1)=729#

#=>(3)^(n-1)=(3)^6#

#=>n-1=6#

#=>n=7#

#"Sum of first n-terms is :"#

#S_n=(a_1(r^n-1))/(r-1)#

#=>S_7=(4(3^7-1))/(3-1)#

#=>S_7=(4(2187-1))/2#

#=>S_7=2(2186)#

#=>S_7=4372#