Find the next number in the series:

2, 17, 89, 359, 1079, ?

Question

Find the next number in the series:

2, 17, 89, 359, 1079, ?

Accepted Answer

**Solution:**

1. Given series: 2, 17, 89, 359, 1079, ?

2. Let's analyze the pattern by checking the difference between consecutive terms:

- 17 - 2 = 15
   - 89 - 17 = 72
   - 359 - 89 = 270
   - 1079 - 359 = 720

3. Now, look at the differences: 15, 72, 270, 720

4. Check if these differences follow a pattern:

- 15 = 1 × 3 × 5
   - 72 = 2 × 3 × 12
   - 270 = 3 × 3 × 30
   - 720 = 4 × 3 × 60

This is not straightforward, so try another approach.

5. Check the ratio of consecutive terms:

- 17 / 2 = 8.5
   - 89 / 17 ≈ 5.24
   - 359 / 89 ≈ 4.03
   - 1079 / 359 ≈ 3.01

Ratios are decreasing roughly by 1.5, 1.2, 1.0.

6. Another approach is to check if each term is generated by multiplying the previous term by an integer and then adding or subtracting a number:

- 2 × 8 + 1 = 17
   - 17 × 5 + 4 = 89
   - 89 × 4 + 3 = 359
   - 359 × 3 + 2 = 1079

7. Following this pattern, the next term should be:

- 1079 × 2 + 1 = 2159

**Answer:** 2159

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