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an arithmetic sequence with first term $1$ has a common difference of $6$. a second sequence begins with $4$ and has a common difference of $7$. in the range of $1$ to $100$, what is the largest number common to both sequences?

Answer :

The largest number common to both sequences is 67.

The arithmetic sequence with first term 1 has a common difference of 6 is given by:-

1,7,13,19, 25, 31, 37, 43, 49, 55, 61, 67, 73, 79, 85, 91, and 97

The arithmetic sequence with first term 4 has a common difference of 7 is given by:-

4,11, 18, 25, 32, 39, 46, 53, 60, 67, 74, 81, 88, and 95.

I have written the sequence until 100 only.

Hence, the numbers common to both the arithmetic sequences are :-

25 and 67

Hence, the largest number common to both sequences is 67.

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https://brainly.com/question/10396151

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