Determine the arithmetic sequence whose terms is 17 over 12 and eighteenth term is 59 over 12 with solution please​

Answer:To determine the arithmetic sequence with the first term \( a_1 = \frac{17}{12} \) and the eighteenth term \( a_{18} = \frac{59}{12} \), we'll find the common difference \( d \) and then express the general term of the sequence.### Step 1: Use the formula for the 18th termThe formula for the \( n \)th term of an arithmetic sequence is:\[a_n = a_1 + (n-1) \times d\]For the 18th term:\[a_{18} = a_1 + 17d\]Substituting the known values:\[\frac{59}{12} = \frac{17}{12} + 17d\]### Step 2: Solve for \( d \)Subtract \( \frac{17}{12} \) from both sides:\[\frac{59}{12} - \frac{17}{12} = 17d\]Simplify:\[\frac{42}{12} = 17d\]\[\frac{7}{2} = 17d\]Divide by 17:\[d = \frac{7}{34}\]Final AnswerThe common difference \( d \) is \( \frac{7}{34} \), and the general formula for the \( n \)th term of the sequence is:\[a_n = \frac{17}{12} + (n-1) \times \frac{7}{34}\]

Answered by vonvigonte21 | 2024-09-04