Question

Consider the following alphanumeric series with powers:
A¹, C³, E⁵, G⁷, __, __, I⁹, __,K¹¹, M¹³, __
Based on the observed pattern, complete the series by selecting the correct options: 
 

• A. \(N^{15},\ P^{17}\)
• B. \(H^{9},\ J^{11}\)
• C. \(Q^{15},\ S^{17}\)
• D. \(O^{15},\ Q^{17}\)

Hint:

For alphanumeric series, check if letters move by a fixed step in the alphabet and whether exponents track a simple numerical pattern (e.g., odd numbers or alphabetical indices).

Answer 1

The Correct Option is D

Step 1 (Read the joint pattern of letters and exponents).
Look at the letters: \(A, C, E, G, \ldots\) — they increase by skipping one letter each time (\(+2\) positions in the alphabet). So the letter sequence must be: \[ A,\ C,\ E,\ G,\ {I},\ {K},\ M,\ {O},\ {Q},\ldots \]

Step 2 (Match the exponents).
The powers are \(1,3,5,7,\ldots\) — consecutive odd numbers, which also equal each letter’s alphabetical index: \(A=1,\ C=3,\ E=5,\ G=7,\ I=9,\ K=11,\ M=13,\ O=15,\ Q=17\).

Step 3 (Fill the blanks).
Thus the full series is: \[ A^{1},\ C^{3},\ E^{5},\ G^{7},\ {I^{9}},\ {K^{11}},\ I^{9}\ (\text{already given later}),\ {O^{15}},\ K^{11}\ (\text{given}),\ M^{13},\ {Q^{17}}. \] Interpreting the intended progression (ignoring the out-of-place repeats provide(d), the correct two missing terms at the end after \(M^{13}\) are \({O^{15},\ Q^{17}}\).

Step 4 (Compare with options).
None of the options \((a)\ N^{15},P^{17;\ }(b)\ H^{9},J^{11;\ }(c)\ Q^{15},S^{17;\ }(d)\ I^{9},K^{11}\) matches \({O^{15}, Q^{17}}\).
\[ {\text{O}^{15},\ \text{Q}^{17}\ \text{(not listed among the options)}} \]