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The number of common terms to the two sequences and is
Full solution
Q. The number of common terms to the two sequences and is
- Identify Pattern: First, let's identify the pattern in each sequence.The first sequence starts at and increases by each time (, , , ...).The second sequence starts at and increases by each time (, , , ...).We need to find the common terms in these sequences.
- Find nth Term Formula: Let's find the nth term formula for each sequence.For the first sequence, the nth term can be given by:where is the first term and is the common difference.For the first sequence, and .So,
- Solve for Common Terms: For the second sequence, the th term () can be given by:where is the first term and is the common difference.For the second sequence, and .So,
- Correct Mistake: Now, we need to find the common terms, which means we need to solve for where . So we set the nth term equations equal to each other:
- Correct Mistake: Now, we need to find the common terms, which means we need to solve for where . So we set the nth term equations equal to each other: Solving the equation for : This is incorrect because we made a mistake in the simplification process. Let's correct it.
