A geometric series has a first term of 12 and a constant ratio of one third. What is its sum to infinity?

1. A sum to infinity only exists if the series converges, so test the ratio first. 2. The constant ratio is one third, which lies between minus one and one, so the series converges. 3. The sum to infinity of a converging geometric series is the first term divided by one minus the ratio. 4. One minus one third is two thirds. 5. So the sum is 12 divided by two thirds. 6. Dividing by two thirds is the same as multiplying by three halves, so the sum is 12 multiplied by 1.5. 7. That gives a sum to infinity of 18. 8. The answer 36 traps anyone who divides by the ratio itself instead of by one minus the ratio, the answer 4 multiplies by the ratio, and the answer 24 doubles the first term. _Source: Siyavula Mathematics Grade 12 (Everything Maths, CC BY 4.0), Chapter 1: Sequences and series_