Arithmetic — nth Term

Free interactive math game: Arithmetic — nth Term — a₁₀ = ?. Part of the Sequences category on MathKite.

Example problems

Taken from the generator that powers this exercise. A fresh set appears every time the page is opened, and the printable worksheet holds ten of them.

  1. In an arithmetic sequence: a₁ = 0, d = 2 Find a₁₅ = ?
  2. In an arithmetic sequence: a₁ = 1, d = 5 Find a₁₅ = ?
  3. In an arithmetic sequence: a₁ = 8, d = 4 Find a₈ = ?
  4. In an arithmetic sequence: a₁ = -3, d = 8 Find a₁₅ = ?

About this exercise

Finding a distant term of an arithmetic sequence without listing them all.

How to solve it

Start from the first term and add the common difference one time fewer than the position number.

Worked example

Starting at 5 with a difference of 3, the tenth term is 5 + 9 x 3 = 32.

Common mistake

Multiplying by the position itself. The first term already counts as one, so the multiplier is n - 1.