Sure! Here’s the extracted text: --- Q.12) A sequence of terms is defined as follows: \( T_1 = 1, T_2 = 4 + 4^2 + 4^3, T_3 = 4^4 + 4^5 + 4^6 + 4^7 + 4^8, T_4 = 4^9 + 4^{10} + 4^{11} + 4^{12} + 4^{13} + 4^{14} + 4^{15}, \) and so on. Find the sum of first 12 terms of the sequence. a) \( \frac{4^{143} - 1}{3} \) b) \( \frac{4^{100} - 1}{3} \) c) \( \frac{4^{100} + 1}{3} \) d) \( 4^{121} \left(4^{23} - \frac{1}{3}\right) \) e) None of these ---