Dawnbridge

TI-Nspire CX II field manual for IB Math

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9

Working with sequences

All courses

Enter a sequence, open its table, and scroll until the first row where the sequence value is greater than a chosen threshold.

Goal

Find the first value of ​n​ for which the sequence ​un​=10(1.2)n​ exceeds ​1000.

1

Open the Scratchpad's Graph view ( → B: Graph Scratchpad). Change the graph type to a sequence: → 3: Graph Entry/Edit → 7: Sequence → 1: Sequence. On u1(n)=, type 10*1.2^n with and press . Because the sequence is explicit, no initial-value line is needed.

Scratchpad
RAD
u1(n)=10∗1.2nInitial Terms:=1≤n≤99 nstep=1
2

Show the function table with and scroll down until the sequence first passes ​1000. The value at ​n=25​ is still below the target, and the next value is the first one above it. (The default table settings work here; to change the start or step, press → Table → 5: Edit Table Settings.)

Scratchpad
RAD
u1​(n)=10(1.2)n
nu1(n)
22552.061
23662.474
24794.968
25953.962
261144.755
271373.706
Result

The first value is ​n=26, because ​u25​≈954​ but ​u26​≈1140.

Your turn

Work each one on your calculator, then check the answer.

  1. 1

    Find the first ​n​ for which ​un​=5(1.3)n​ exceeds ​2000.

  2. 2

    Find the first ​n​ for which ​un​=4n(1.1)n​ exceeds ​600.

  3. 3

    Find the first ​n​ for which ​un​=8(1.25)n​ exceeds ​300.