Find First Term (Arith.)

Free interactive math game: Find First Term (Arith.) — Find a₁. 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: d = 7, a₁₀ = 67 Find a₁ = ?
  2. Arithmetic sequence: d = -2, a₁₁ = -28 Find a₁ = ?
  3. Arithmetic sequence: d = 6, a₁₁ = 74 Find a₁ = ?
  4. Arithmetic sequence: d = 7, a₁₀ = 54 Find a₁ = ?

About this exercise

Recovering the first term when a later term is known.

How to solve it

Step backwards by subtracting the common difference as many times as needed.

Worked example

If the fifth term is 20 and the difference is 3, the first term is 20 - 4 x 3 = 8.

Common mistake

Stepping back one time too many. From the fifth to the first is four steps, not five.