Running it backward: which term?

Running it backward: which term?

The explicit rule also runs backward: given a term, find its term number. A concert hall has 58 seats in row 1, 62 in row 2, 66 in row 3. Which row has 94 seats?

1. 1Write the explicit rule.a₁ = 58 and d = 4, so a_n = 58 + 4(n − 1).
2. 2Set it equal to the target.58 + 4(n − 1) = 94.
3. 3Solve the Unit 1 way.Subtract 58 from both sides: 4(n − 1) = 36. Divide both sides by 4: n − 1 = 9. Add 1: n = 10.

Row 10 has 94 seats. Check: 58 + 4 × 9 = 58 + 36 = 94. If the answer had not been a whole number, the target would not be a term at all, because term numbers are whole numbers.

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