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
Given the third term and the fourth term for a geometric progression is
1 Answer
Jan 15, 2018
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#