This deep dive covers Finding the nth Term Formula: The 5-Step Method within Quadratic Sequences for GCSE Mathematics. Revise Quadratic Sequences in Algebra for GCSE Mathematics with 12 exam-style questions and 22 flashcards. This topic appears regularly enough that it should still be part of a steady revision cycle. It is section 4 of 8 in this topic. Use this deep dive to connect the idea to the wider topic before moving on to questions and flashcards.
Finding the nth Term Formula: The 5-Step Method
To find the formula an² + bn + c for a quadratic sequence, follow these steps:
Step 1: Calculate First Differences
Find the differences between consecutive terms
Step 2: Calculate Second Differences
Find the differences between the first differences
Step 3: Find coefficient 'a'
a = ½ × (second difference)
Step 4: Create sequence an² and find differences
Calculate the differences between original sequence and an²
Step 5: Find 'b' and 'c'
The differences form a linear sequence bn + c
Practice questions for Quadratic Sequences
Which of the following is a property of a quadratic sequence?
A student says: 'The sequence 3, 7, 13, 21, 31 is quadratic because the first differences increase.' Explain whether the student is correct and how to check properly.