Question

sum of the first two terms of GP is 8 and the first four terms is 80 find the sum of first 6 terms.​

Answer 1

Hey there,

Let the terms in gp be a,ar,ar^2,ar^3

then, a+ar = 8----------(1)

a+ar+ar2+ar3 = 80---------(2)

=> (a+ar)+r2(a+ar) = 80

Using (1)

=> 8+8*r2 = 80

=> 8(1+r2) =80

=> 1+r2 = 10

=> r2=9

therefore. r = 3 (or) -3---------(3)

Using (1)

a+a(3)=8. {for r=3}

=> 4a=8

=> a=2

a+a(-3) =8. {for r= -3}

=> -2a = 8

=> a= -4

Sum of first n terms in gp is Sn = a( r^n -1)/r-1

S6 = 2(3^6 -1)/ 3-1

=> 2(728)/2

=> 728

Therefore,sum of first 6 terms is 728