1 3-5 7 9-11, 13.3n terms ?options a)2n^2 3 b) 5n^2 2 c)3n^2-4n d)3n^2...
Identifying the Pattern
- The given sequence is: 1, 3, 4, 5, 7, 9, 10, 11, 13
- We can see that the sequence consists of consecutive numbers with some gaps in between.
Finding the Differences
- The differences between consecutive terms are: 2, 1, 1, 2, 2, 1, 1, 2
- We notice that the differences are alternating between 1 and 2.
Forming the General Formula
- By observing the pattern, we can deduce that the formula for the sequence can be represented as follows:
- For terms with a difference of 1: 3n - 2 (where n is the term number)
- For terms with a difference of 2: n^2 - 2 (where n is the term number)
Applying the Formula
- Let's find the 3rd term:
- For n = 3, using the formula 3n - 2, we get 7
- Let's find the 5th term:
- For n = 5, using the formula n^2 - 2, we get 23
Options Analysis
- a) 2n^2 + 3: This option does not match the pattern observed in the sequence.
- b) 5n^2 + 2: This option does not match the pattern observed in the sequence.
- c) 3n^2 - 4n: This option matches the pattern observed in the sequence.
- d) 3n^2: This option matches the pattern observed in the sequence.
Conclusion
- The correct options based on the analysis are:
- c) 3n^2 - 4n
- d) 3n^2
Therefore, options c) and d) are potential formulas for the given sequence.