Consider all the sequences we have discussed so far in this chapter. Which ones are arithmetic progressions Class 9
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Consider all the sequences we have discussed so far in this chapter. Which ones are arithmetic progressions Class 9
Question 1.
Consider all the sequences we have discussed so far in this chapter. Which ones are arithmetic progressions and which ones are not? Can you justify your claim? Class 9
Answer:
A sequence is an AP if the difference between consecutive terms is constant.
| Sequence | Terms | Justification | Justification |
| Differences | Conclusion | ||
| Natural Numbers | 1, 2, 3, 4, ... | 1,1,1, … | AP |
| Odd Numbers | 1, 3, 5, 7, … | 2, 2, 2, … | AP |
| Triangular Numbers | 1, 3, 6, 10, … | 2, 3, 4, 5, … | Not AP |
| Square Numbers | 1, 4, 9, 16, … | 3, 5, 7, 9, … | Not AP |
| Virahanka-Fibonacci | 1, 2, 3, 5, 8, 13, … | 1, 1, 2, 3, 5, … | Not AP |
| Growing pattern of squares | 1, 5, 9, 13, … | 4, 4, 4, … | AP |
| 1, 4, 7, 10, ... | 1, 4, 7, 10, … | 3, 3, 3, … | AP |
| 11, 7, 3, -1, ... | 11, 7, 3, -1, … | -4, -4, -4, … | AP |