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A sequence in which any term − its immediate previous term gives a constant is called
a)arithmetic sequences
b)geometric sequences
c)harmonic sequences
d)complex sequences
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
A sequence in which any term − its immediate previous term gives a con...
An arithmetic sequence is a list of numbers with a definite pattern. If you take any number in the sequence then subtract it by the previous one, and the result is always the same or constant.
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A sequence in which any term − its immediate previous term gives a con...
Gives a constant is called comman difference and comman difference explains arithmetic sequence
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A sequence in which any term − its immediate previous term gives a con...
Arithmetic Sequences Explanation
Arithmetic sequences are sequences in which each term is a constant difference from the previous term. This means that if you subtract any term from its immediate previous term, you will always get the same constant value.
Example of Arithmetic Sequences:
For example, the sequence 2, 5, 8, 11, 14 is an arithmetic sequence because the difference between each consecutive term is 3.
Comparison with Other Sequences:
- Geometric sequences: In geometric sequences, each term is a constant multiple of the previous term, not a constant difference.
- Harmonic sequences: In harmonic sequences, the reciprocals of the terms form an arithmetic sequence, but the terms themselves do not form an arithmetic sequence.
- Complex sequences: Complex sequences do not have a specific definition, but arithmetic, geometric, and harmonic sequences are more commonly studied in mathematics.
Therefore, based on the definition provided in the question, a sequence in which any term minus its immediate previous term gives a constant is classified as an arithmetic sequence.
Arithmetic sequences are sequences in which each term is a constant difference from the previous term. This means that if you subtract any term from its immediate previous term, you will always get the same constant value.
Example of Arithmetic Sequences:
For example, the sequence 2, 5, 8, 11, 14 is an arithmetic sequence because the difference between each consecutive term is 3.
Comparison with Other Sequences:
- Geometric sequences: In geometric sequences, each term is a constant multiple of the previous term, not a constant difference.
- Harmonic sequences: In harmonic sequences, the reciprocals of the terms form an arithmetic sequence, but the terms themselves do not form an arithmetic sequence.
- Complex sequences: Complex sequences do not have a specific definition, but arithmetic, geometric, and harmonic sequences are more commonly studied in mathematics.
Therefore, based on the definition provided in the question, a sequence in which any term minus its immediate previous term gives a constant is classified as an arithmetic sequence.
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A sequence in which any term − its immediate previous term gives a constant is calleda)arithmetic sequencesb)geometric sequencesc)harmonic sequencesd)complex sequencesCorrect answer is option 'A'. Can you explain this answer?
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