Advance a recurrence - a loan balance each month, a population each year - without retyping the previous value.
In short: Stepping a recurrence forward means applying a rule such as u(n+1) = a·u(n) + b again and again to generate later terms. You store the first value, enter the rule using the last-answer key, and press ENTER repeatedly. Use it for loans, population growth and Markov problems where each value depends on the one before.
| TI-84 Plus CE | Casio fx-CG50 and fx-CG100 | TI-Nspire CX | |
|---|---|---|---|
| Key sequence | Type the start value, ENTER; then the rule using 2nd → (−) (ANS), e.g. Ans×1.02−200, and press ENTER repeatedly. | In Run-Matrix enter the start value, then the rule using Ans, and press EXE repeatedly; Recursion mode also tabulates aₙ₊₁. | Enter the first value, then a formula referring to the previous answer; press ENTER repeatedly (or use a recursive spreadsheet column). |
Tip: This Ans-recursion trick (rule using the last answer, then repeated ENTER) works for any step-by-step process.
Tip: This Ans-recursion trick (rule using the last answer, then repeated ENTER) works for any step-by-step process.
Tip: This Ans-recursion trick (rule using the last answer, then repeated ENTER) works for any step-by-step process.
Here's a real IB-style question that uses exactly this technique.
A loan balance follows uₙ₊₁ = 1.05uₙ − 100, with u₁ = 1000. Find u₅, to the nearest whole number.
Advance a recurrence - a loan balance each month, a population each year - without retyping the previous value. A recurrence relation describes a loan balance, population or investment changing each period. You need a term several steps ahead without retyping the previous value each time.
1. Write the rule, e.g. nextBalance = balance × 1.02 − 200, and the starting value. 2. Type the start value, ENTER; then the rule using 2nd → (−) (ANS), e.g. Ans×1.02−200, and press ENTER repeatedly. 3. Each ENTER/EXE gives the next term - count the presses to reach the term you need.
1. Write the rule, e.g. nextBalance = balance × 1.02 − 200, and the starting value. 2. In Run-Matrix enter the start value, then the rule using Ans, and press EXE repeatedly; Recursion mode also tabulates aₙ₊₁. 3. Each ENTER/EXE gives the next term - count the presses to reach the term you need.
1. Write the rule, e.g. nextBalance = balance × 1.02 − 200, and the starting value. 2. Enter the first value, then a formula referring to the previous answer; press ENTER repeatedly (or use a recursive spreadsheet column). 3. Each ENTER/EXE gives the next term - count the presses to reach the term you need.
This Ans-recursion trick (rule using the last answer, then repeated ENTER) works for any step-by-step process.
In the worked example on this page (3 marks, Paper 2), the marks are: M1: Step the recurrence forward 4 times from u₁; A1: 784.
Questions that need this technique link back to this guide. Try one in practice mode, or see every GDC guide.