How to answer these using geometric progression formula ?

Given the third term and the fourth term for a geometric progression is #75 and 375# respectively. Find the sum of the first seven terms after the third term

1 Answer
Jim G.
Jan 15, 2018

#7324125#

Explanation:

#"using the following formulae"#

#•color(white)(x)a_n=ar^(n-1)#

#•color(white)(x)S_n=(a(r^n-1))/(r-1)#

#a_3=ar^2=75to(1)#

#a_4=ar^3=375to(2)#

#"divide equation "(2)" by equation "(1)#

#(ar^3)/(ar^2)=375/75rArrr=5#

#"substitute "r=5" in equation "(1)#

#rArr25a=75rArra=3#

#"sum of "a_4toa_(10)=S_(10)-S_3#

#=(3(5^(10)-1))/4-(3(5^3-1))/4#

#=7324218-93=7324125#

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