The given sequence is Geometric Progression. Ratio of any term to its preceding term is 1:3 so common ratio is 1/3 i.e. r = 1/3.
First term is 729 i.e. a = 729.
Now, we need to find the sixth and seventh terms.
nth term of a G.P. is given by an = arn-1.
So, a6 = 729 x (1/3)6-1 = 729/243 = 3.
a7 = 729 x (1/3)7-1 = 729/729 = 1.
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1 x 729, 3 x 243, 9 x 81, 27 x 27
3 = 3^(1) 9 = 3(2) ??? = 3^(3) 81 = 3^(4) 243 = 3^(5) 729 = 3^(6) There are TWO missing numbers !!! They are 3^(3) = 27 & 3^(0) = 1 1 = 3^(0) 3 = 3^(1) 9 = 3(2) 27 = 3^(3) 81 = 3^(4) 243 = 3^(5) 729 = 3^(6)
1 x 243, 3 x 81, 9 x 27.
How about: 2*243 = 486 as one example
2/3 x 729 = 486