Explanation
The correct answer is option (C), i.e. the next term will be I^27/2 R162. There are two different patterns at work in this sequence. If we look at the order of the first letters, it is A(1), C(3), E(5), G(7), which increases by 2 letters each time, so the next letter will be I(9). Similarly, the order of exponents (powers) is 3/2, 9/2, 15/2, 21/2, which increases by 6/2 i.e. 3 each time, hence the next exponent will be 27/2. In the second part the order of letters is B(2), F(6), J(10), N(14) which advances by 4 letters each time, so the next letter will be R(18). The numbers that follow are in the pattern of 2(2×1²), 18(2×3²), 50(2×5²), 98(2×7²), which represent twice the square of the odd numbers (1,3,5,7), so the next number will be 2×9² = 162. Thus the next term becomes I^27/2 R162, which matches option (C).