Question

27+9+3+1.........12terms

Answer 1

27,9,3,1 .... given series
a2/a1 = 9/27 =1/3---(1)

a3/a2 = 3/9 =1/3----(2)
therefore
(1) = (2)
27,9,3,1... is in geometric progression
first term =a = 27

common ratio = r =a3/a2 = 1/3 [ r <1]

sum of n terms = sn = a(1-r^n)/ (1-r)

here a = 27, r= 1/3, n= 12

s12 = 27[1- (1/3)^12]/(1-1/3)

= 27 [(3^12 - 1)/3^12]/ (2/3)
=27[3^12 - 1]/3^12 * 3/2

= [3^12-1]/2*3^8