Dawnbridge

TI-84 Plus CE field manual for IB Math

Everyone · 9 of 45

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

Press . From the default cursor position, press four times to reach the FUNCTION PARAMETRIC POLAR SEQ row, then three times to reach SEQ, and press .

2

Press . Press to move to the nMin= line, then type to set nMin=1.

3

Press to move to u(n)=, then type 10(1.2)^n with . Leave u(1) blank because this is an explicit sequence, not a recursive one.

NORMALFLOATAUTOREALRADIANMP
Plot1Plot2Plot3
TYPE:SEQ(n)SEQ(n+1)SEQ(n+2)
nMin=1
\u(n)=10(1.2)n
u(1)=
u(2)=
\v(n)=
v(1)=
v(2)=
\w(n)=
4

Open table setup with and set TblStart=1 (the default is 0) so the table matches nMin. Keep the other defaults shown below. Then press to view the table.

NORMALFLOATAUTOREALRADIANMP
TABLE SETUP
TblStart=1
ΔTbl=1
Indpnt:AutoAsk
Depend:AutoAsk
5

The table starts at ​n=1. Press to scroll until the values pass ​1000: the row for ​n=25​ is still below the target, and the next row is the first one above it. (To jump ahead instead of scrolling, reopen table setup with and raise TblStart to a value near the target.)

NORMALFLOATAUTOREALRADIANMP
PRESS + FOR ΔTbl
nu23662.47424794.96825953.962261144.75271373.71
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.