Find Position (Arith.)

Free interactive math game: Find Position (Arith.) — Which term?. 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. Arithmetic sequence: a₁ = 10, d = 7 Which term equals 87?
  2. Arithmetic sequence: a₁ = 4, d = 7 Which term equals 102?
  3. Arithmetic sequence: a₁ = 7, d = 7 Which term equals 42?
  4. Arithmetic sequence: a₁ = 5, d = 3 Which term equals 29?

About this exercise

Finding where a given value sits in a sequence.

How to solve it

Subtract the first term from the value, divide by the common difference, then add one.

Worked example

In 4, 7, 10 the value 25 sits at (25 - 4) : 3 + 1 = 8.

Common mistake

Forgetting the final plus one. Without it you have counted the steps, not the position.