Check whether √5, √20, √45, √80, ... forms an AP. If it does, find its common difference and its next two terms.

1. 1 · Write what is given and what is to be found. Given: the list √5, √20, √45, √80, ... To find: whether it is an AP, its d and the next two terms.
2. 2 · Write the formula or theorem. A list is an AP if each term minus the term before it gives the same number d.
3. 3 · Simplify the terms. √20 = 2√5, √45 = 3√5, √80 = 4√5. So the list is √5, 2√5, 3√5, 4√5, ...
4. 4 · Find every difference.
   • a₂ − a₁ = 2√5 − √5 = √5
   • a₃ − a₂ = 3√5 − 2√5 = √5
   • a₄ − a₃ = 4√5 − 3√5 = √5
   • All equal, so it is an AP with d = √5.
5. 5 · Find the next two terms. a₅ = 4√5 + √5 = 5√5 = √125 and a₆ = 6√5 = √180.
6. 6 · Check and box the answer. Yes, it is an AP. d = √5. Next two terms: √125 and √180.

Scoring tip: Show at least three differences. Stopping after one pair loses the method mark.