In the following question, a number series is given with one term missing. Select the missing number from the series that correctly continues the pattern: 7, 19, 42, 87, ?

Introduction / Context:
This question presents a non linear series 7, 19, 42, 87, ?. The pattern involves both multiplication and addition, with the additive part gradually decreasing. Such series are widely used in reasoning tests to check attention to detail and the ability to detect changing operations between terms.

Given Data / Assumptions:

• Series: 7, 19, 42, 87, ?
• Options: 136, 176, 172, 216.
• We assume the same transformation pattern applies to each consecutive pair of terms.

Concept / Approach:
The numbers are roughly doubling at each step but not exactly. This suggests a rule of the form T(n+1) = 2 * T(n) + or - some small integer. If that small integer decreases in a regular way, we can identify the pattern and extend it. We therefore test whether each term can be written as twice the previous term plus a decreasing constant.

Step-by-Step Solution:
Step 1: Relate the second term to the first.19 = 2 * 7 + 5.Step 2: Relate the third term to the second.42 = 2 * 19 + 4.Step 3: Relate the fourth term to the third.87 = 2 * 42 + 3.Step 4: Identify the pattern in the constants.The added constants are 5, 4, 3, which decrease by 1 each time.Step 5: Apply the same pattern to find the next term.Next constant should be 2.Missing term = 2 * 87 + 2 = 174 + 2 = 176.

Verification / Alternative check:
With the completed series 7, 19, 42, 87, 176, we can re express it as: 7, 2 * 7 + 5, 2 * 19 + 4, 2 * 42 + 3, 2 * 87 + 2. The pattern of adding 5, 4, 3, 2 after doubling is consistent and regular. There is no contradiction or irregular step, confirming that 176 is the correct next term in the series.

Why Other Options Are Wrong:
136: 2 * 87 + constant would require adding -38, which does not match the decreasing constant pattern 5, 4, 3, 2.172: Would require adding -2 to 2 * 87, which does not follow the rule of decreasing positive additions.216: Would correspond to 2 * 87 + 42, completely unrelated to the observed constants.

Common Pitfalls:
Some candidates look only at raw differences (12, 23, 45) and find that pattern too messy. A better method for such fast growing sequences is to consider whether each term is approximately double the previous one and then refine with small adjustments. Noticing that the adjustments 5, 4, 3 are decreasing by 1 makes the series easy to extend and avoids guesswork.

Final Answer:
The missing number that continues the pattern 2 * previous term plus a decreasing constant is 176.