First of all, let us define the x^{th} term.
3^{3+6+9+……….3x } = (0.)^{-66}
Whenever you encounter a distinctive number such as one given in R.H.S of above equation, always try to find its significance in the context of question. In this case L.H.S has 3^{power}, so (0.) must be some form of 3^{power}.
With little hit and trial, you may find
3^{3(1 + 2 + 3 + ...X)} = 3^{ -3 * -66}
=> 3^{3*66}
x(x+1) = 132
Solving this equation for x > 0, we get x= 11. You should directly be able to see that 132 = 11 x 12 =) x= 11
And avoid wasting time solving the complete equation.
Correct Answer is (D)
Correct Answer: 11
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