BANK & INSURANCE (WRONG NUMBER SERIES PART 1)

600 - (1² + 2²) = 600 - 5 = 595

595 - (2² + 3²) = 595 - 13 = 582

582 - (3² + 4²) = 582 - 25 = 557

557 - (4² + 5²) = 557 - 41 = 516

516 - (5² + 6²) = 516 - 61 = 455 ≠ 442

442 is the wrong number, should be 455.

20 + (1×2) = 20 + 2 = 22

22 + (3×4) = 22 + 12 = 34

34 + (5×6) = 34 + 30 = 64

64 + (7×8) = 64 + 56 ≠ 144

Pattern says next is + (9×10) = 90

144 + (9×10) = 144 + 90 = 234 ≠ 210

210 + (11×12) = 210 + 132 = 342

Pattern fits; 144 is the wrong number, should be 120 (64 + 56) .

Differences follow the pattern: n³ − (n−1)²

2³ − 1² = 8 − 1 = 7
3³ − 2² = 27 − 4 = 23
4³ − 3² = 64 − 9 = 55
5³ − 4² = 125 − 16 = 109
6³ − 5² = 216 − 25 = 191

So correct differences should be: 7, 23, 55, 109, 191

But given last difference is 126 (incorrect).

Correct last term

294 + 191 = 485, So correct last term should be 485.

Answer: 420 is the wrong term.

Find the differences

204 − 200 = 4
222 − 204 = 18
270 − 222 = 48
320 − 270 = 50
550 − 320 = 230

Observe carefully:

4 = 1 × 2² = 1 × 4 = 4
18 = 2 × 3² = 2 × 9 = 18
48 = 3 × 4² = 3 × 16 = 48
100 = 4 × 5² = 4 × 25 = 100
180 = 5 × 6² = 5 × 36 = 180

So correct differences should be: 4, 18, 48, 100, 180

Check the series using correct differences

200 + 4 = 204
204 + 18 = 222
222 + 48 = 270
270 + 100 = 370
370 + 180 = 550

So correct series should be: 200, 204, 222, 270, 370, 550

But given term is 320 instead of 370.

46 + 2² = 46 + 4 = 50

50 - 3³ = 50 - 27 = 23

23 + 4² = 23 + 16 = 39

39 - 5³ = 39 - 125 = -86 ≠ -78

-78 + 6² = -78 + 36 = -42 ≠ -50

Pattern fits; -78 is the wrong number, should be -86 😊

Pattern difference decreasing:
+243, +81, +29, +7, +3 (not systematic)
Actual pattern: +243, +81, +27, +9, +3
Correct 336+27=363 (not 365)
Wrong term: 365