In the following question, select the missing number from the given series, which uses steadily increasing increments. 23, 28, 34, 41, 49, ?

Introduction / Context:
This number series gradually increases, with the gaps between terms themselves growing in a simple pattern. The learner must compute the step between each term and recognise that these steps increase by a constant amount. This is a classic example of using second level differences to determine the next term.

Given Data / Assumptions:
- Series: 23, 28, 34, 41, 49, ? - The sixth term is missing. - The differences between terms appear to increase gradually.

Concept / Approach:
First compute the difference between each pair of consecutive terms. Then examine whether these differences follow their own pattern, such as increasing by 1 each time. Once this secondary pattern is known, it can be extended to find the next difference, which in turn gives the missing term.

Step-by-Step Solution:
Step 1: Compute differences. 28 - 23 = 5. 34 - 28 = 6. 41 - 34 = 7. 49 - 41 = 8. Step 2: The differences are 5, 6, 7, and 8, increasing by 1 each time. Step 3: The next difference in this sequence should be 9. Step 4: Add this difference to the last known term: 49 + 9 = 58.

Verification / Alternative check:
Reconstruct the series using the difference pattern: starting from 23, add 5, 6, 7, 8, and 9. This yields 28, 34, 41, 49, and 58. The pattern of increasing differences remains perfectly consistent, confirming 58 as the correct next term.

Why Other Options Are Wrong:
- Option 59 would require a difference of 10 from 49, which would skip the expected increase of 9. - Option 57 gives a difference of 8, repeating the last difference instead of increasing it by 1. - Option 56 gives a difference of 7 and clearly breaks the upward trend of the differences.

Common Pitfalls:
Some learners may only look for a constant difference and miss the gradually increasing nature of the increments. Others may miscalculate a difference and fail to see the clear pattern of plus 1 each time. Checking the sequence of differences carefully helps avoid such errors.

Final Answer:
The missing term in the series is 58, so the correct option is 58.