Arithmetic Sequence nth Term

an=a1+(n1)da_n = a_1 + (n - 1) d

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An arithmetic sequence climbs (or falls) by the same amount every step, so the nth term is just the first term plus (n − 1) copies of the common difference d. Theater rows work this way: if row 1 has 20 seats and each row adds 3 more, row 12 has 20 + 11 × 3 = 53 seats.

Run it backward to locate a value: with a₁ = 5 and d = 4, the term equal to 45 sits at n = (45 − 5)/4 + 1 = 11. If that comes out fractional, the value simply never appears in the sequence.

Arithmetic Sequence nth Term
an=a1+(n1)da_n = a_1 + (n - 1) d
Where
  • ana_n= nth term
  • a1a_1= First term
  • nn= Term number
  • dd= Common difference
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