Examine the pattern \( 7 ; 12 ; 17 ; 22 ; \) J. Determine a formula for the general rule for the \( n^{\text {th }} \) term of the k. Determine the \( 58^{\text {th }} \) term of the pattern. I. Which term of the pattern is equal to 4170
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The pattern you've provided is an arithmetic sequence where each term increases by 5, starting from 7. The general formula for the \( n^{\text{th}} \) term can be expressed as \( a_n = 7 + (n - 1) \cdot 5 \), which simplifies to \( a_n = 5n + 2 \). To find the \( 58^{\text{th}} \) term, substitute \( n = 58 \) into the formula: \( a_{58} = 5 \cdot 58 + 2 = 290 + 2 = 292 \). To determine which term equals 4170, set the general formula equal to 4170: \( 5n + 2 = 4170 \). Solving for \( n \) gives \( n = \frac{4170 - 2}{5} = \frac{4168}{5} = 833.6 \). Since \( n \) must be a whole number, there is no term in this pattern that equals 4170.
