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In an arithmetic sequence, the first term is 7 and each term after the first is 4 more than the term before it. What is the 20th term of the sequence?
83 (choice C). The nth term is the first term plus (n − 1) steps: 7 + (20 − 1) × 4 = 7 + 76 = 83. There are only 19 steps of 4 between the 1st term and the 20th.
We posted this ACT-style question on Facebook and Instagram with the line “The setup is the whole question.” The question was written by Brainrise; it is not an official ACT item.
The classic slip is multiplying by 20 instead of 19: 7 + 20 × 4 = 87, which is one of the choices. Another is reporting the total added, 76, instead of the term itself. Counting the steps between terms, not the terms, avoids both.
Why is 87 wrong?
87 is 7 + 20 × 4. It adds 4 twenty times, but the first term already counts as term 1, so only 19 additions of 4 get you to the 20th term.
Is there a formula to remember?
Yes: aₙ = a₁ + (n − 1)d, where a₁ is the first term and d is the common difference. Here a₁ = 7, d = 4 and n = 20, which gives 83.
What does it cost to practice ACT math in Brainrise?
The 7-day free trial requires a card; after the trial it is $24 a month for one exam (SAT or ACT) or $36 a month for both, and you can cancel any time. Brainrise is not available to New York residents.
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