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Directions: Study the information given carefully and answer the following questions.
In the following question, a number series is given, after the number series, a number and then A, B, C, D and E are given. Complete the number series starting from the given number, based on the pattern of the original number series and choose correct options.
1 226 482 77 1 1095 1456
12 A B C D E
What will come in place of ‘E’?
1235
1465
1467
1764
1567
- Let's examine the initial series: 1, 226, 482, 771, 1095, 1456.
- The numbers increase progressively, though not consistently linear, which suggests a pattern or formula governs their progression.
- Start by examining the differences between consecutive numbers:
- 226 - 1 = 225
- 482 - 226 = 256
- 771 - 482 = 289
- 1095 - 771 = 324
- 1456 - 1095 = 361
- Notice these differences: 225, 256, 289, 324, 361, are perfect squares of consecutive integers: 15², 16², 17², 18², 19².
- The task suggests starting with a given number and applying this pattern: 12, then A, B, C, D, E.
- Start with 12:
- 12 + 15² = 237, so A = 237
- 237 + 16² = 493, so B = 493
- 493 + 17² = 782, so C = 782
- 782 + 18² = 1106, so D = 1106
- 1106 + 19² = 1467, so E = 1467
- Therefore, option 3, 1467, is correct.
Option:3 - 1467
.
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