Correct option is: (3) 14
\(3^9+3^{12}+3^{15}+3^n\)
\(= 3^9 + 3^9 \times 3^3 + 3^9 \times 3^6 + 3^9 \times 3^{n-9}\)
\(=3^9(1+3^3+3^6+3^{n-9})\)
\(1+3^3+3^6+3^{n-9}=1000\)
\(1+27+729+3^{n-9}= 1000\)
\(757 + 3^{n-9}=1000\)
\(3^{n-9}=1000-757\)
\(3^{n-9}=243\)
\(3^{n-9}=3^5\)
\(n-9=5\)
\(n=5+9\)
\(\therefore \ n=14\)
