In the following question, select the missing number from the given series: 470, 465, 460, 455, ?, 445

Introduction / Context:
This is a straightforward arithmetic series where each term decreases by a fixed amount. Such questions test quick recognition of constant differences between consecutive terms. The given sequence is 470, 465, 460, 455, ?, 445, and we are asked to supply the missing number.

Given Data / Assumptions:
- Terms: 470, 465, 460, 455, ?, 445.- Only the fifth term is missing.- The numbers are close together and appear to follow a simple linear pattern.- The most likely rule is subtraction of the same value at each step.

Concept / Approach:
To identify an arithmetic series, we compute successive differences and see if they are constant. If the pattern holds across several steps, we then apply the same difference to find any missing term. Here the series appears to decrease smoothly, so we expect a constant negative difference.

Step-by-Step Solution:
- Difference from 470 to 465: 465 - 470 = -5.- Difference from 465 to 460: 460 - 465 = -5.- Difference from 460 to 455: 455 - 460 = -5.- The pattern is a constant decrease of 5.- Therefore, the next term after 455 is 455 - 5 = 450.- Check the final term: 450 - 5 = 445, which matches the series.

Verification / Alternative check:
- With the missing term as 450, the series becomes 470, 465, 460, 455, 450, 445.- Every step from left to right subtracts exactly 5.- No other candidate preserves this perfectly constant difference.

Why Other Options Are Wrong:
- 448, 440 and 452 would give differences that are not equal to -5 and would disrupt the regular pattern.- 460 is already present in the series as the third term and does not fit between 455 and 445 when we enforce a constant step of -5.

Common Pitfalls:
- Failing to compute differences carefully and misreading the steps as -4 or -10 can lead to incorrect answers.- Overthinking a very simple linear pattern sometimes causes candidates to search for needless complexity.- Ignoring the consistency of differences from multiple positions can result in choosing a value that fits locally but not globally.

Final Answer:
The series decreases by 5 at each step, so the missing term is 450.