Correct Option: B) 102 To identify the pattern in the given number series, we will analyze the differences between consecutive terms. **Step 1: Calculate the first layer of differences between consecutive terms.** * Difference between the 2nd and 1st term: $12 - 7 = 5$ * Difference between the 3rd and 2nd term: $22 - 12 = 10$ * Difference between the 4th and 3rd term: $39 - 22 = 17$ * Difference between the 5th and 4th term: $65 - 39 = 26$ This gives us a new series of differences: $5, 10, 17, 26, \ldots$ **Step 2: Calculate the second layer of differences from the series obtained in Step 1.** * Difference between the 2nd and 1st term of the new series: $10 - 5 = 5$ * Difference between the 3rd and 2nd term of the new series: $17 - 10 = 7$ * Difference between the 4th and 3rd term of the new series: $26 - 17 = 9$ This gives us a second layer of differences: $5, 7, 9, \ldots$ **Step 3: Identify the pattern in the second layer of differences.** The series $5, 7, 9, \ldots$ is an Arithmetic Progression (AP) where each term is obtained by adding 2 to the previous term. The common difference of this AP is $2$. **Step 4: Determine the next term in the second layer of differences.** Following the established pattern, the next term in the second layer of differences will be $9 + 2 = 11$. **Step 5: Determine the next term in the first layer of differences.** To find the next term in the first layer of differences, we add the value from Step 4 to the last term of the first layer: $26 + 11 = 37$. **Step 6: Determine the next term in the original series.** Finally, to find the next term in the original series, we add the value from Step 5 to the last known term of the original series: $65 + 37 = 102$ Thus, the next term in the series is $102$.