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Precalculus

Sum a sequence or series

Add up the first terms of a sequence, such as 1 + 3 + 5 + … + 19, which comes to 100.

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A series is a sum of the terms of a sequence. The odd numbers 1, 3, 5, … have terms 2k − 1. Adding the first ten gives 100.

Many models have a sigma (Σ) template: you give the formula, a start number and an end number. For an arithmetic series you can also use the formula n × (first + last) ÷ 2.

Classic Graphing 84

Start on the main screen: Press 2nd then mode (QUIT) to get back to the home screen. Pressing clear on a menu also backs out of it.

  1. Type sum( by pressing 2nd, stat, then left to MATH and 5. Then type seq( with 2nd, stat, right to OPS and 5.

    2ndLISTstat◀52ndLISTstat▶5

  2. Fill in seq(2X − 1, X, 1, 10) and close both brackets, then press enter.

    2X,T,θ,n−1,X,T,θ,n,1,10))enter

You should seesum(seq(2X−1,X,1,10)) 100

Classic Graphing 84 key reference

Classic Scientific 30

Start on the main screen: Press 2nd then mode (QUIT) to leave any menu or screen and return to the calculation screen.

  1. Open the math menu and pick 4 for the Σ template. Type 2, the variable key, minus 1. Then use the right arrow to move to the start (1) and the end (10).

    math42x yzt abcd−1▶1▶10

  2. Press enter.

    enter

You should seeΣ(2x−1,1,10) 100

Classic Scientific 30 key reference

Natural Scientific 991

Start on the main screen: Press MENU, then 1 (Calculate) to return to the main calculation screen. AC clears the line you are on.

  1. Press SHIFT then the log□ key for Σ. Type 2, ALPHA and the ) key for x, then minus 1. Use the right arrow to move to the start (1) and the end (10).

    SHIFTΣlog2ALPHAx)−1▶1▶10

  2. Press =.

    =

You should seeΣ(2x−1,1,10) 100

Natural Scientific 991 key reference

Natural Color Graphing

Start on the main screen: Press MENU then 1 to open Run-Matrix, the main calculation screen. Press EXIT to back out of a bar or screen, and SHIFT then EXIT (QUIT) to return to the app start.

  1. Press F4 (MATH), then F5 for the Σ( template. Type 2, X, minus 1. Use the right arrow to move to the start (1) and the end (10).

    F4F52X,θ,T−1▶1▶10

  2. Press EXE.

    EXE

You should seeΣ(2X−1,1,10) 100

Natural Color Graphing key reference

Classic CAS

Start on the main screen: Press home to open the Home menu (Calculator, Graphs, Settings, and more). Choose Calculator, or press esc to go back to the calculation page.

  1. Press templates and pick the sum template (entry B). The first box is the counter k. Move with the right arrow: start 1, end 10, then the formula 2k − 1.

    templatesbk▶1▶10▶2k−1

  2. Press enter.

    enter

You should seeΣ(2k−1,k,1,10) 100

Classic CAS key reference

RPN Scientific 15 · Arithmetic series formula

Start on the main screen: There is no menu to leave. Press the back arrow to clear a number you are typing, or CLx (g then back arrow) to clear the X register.

  1. Use n × (first + last) ÷ 2. Key in 10 ENTER 1 ENTER 19, press +, then ×, then 2 ÷.

    10ENTER1ENTER19+×2÷

You should see100.0000

RPN Scientific 15 key reference

RPN Advanced 42 · Arithmetic series formula

Start on the main screen: Press EXIT (once or twice) to close any menu and return to the plain stack view of Y and X.

  1. Use n × (first + last) ÷ 2. Key in 10 ENTER 1 ENTER 19, press +, then ×, then 2 ÷.

    10ENTER1ENTER19+×2÷

You should seex: 100.0000

RPN Advanced 42 key reference

RPN Power 48 · Arithmetic series formula

Start on the main screen: Press ON to cancel what you are typing, then use the stack view. Open the MODE or VAR menu any time; the stack is always shown above the menu row.

  1. Use n × (first + last) ÷ 2. Key in 10 ENTER 1 ENTER 19, press +, then ×, then 2 ÷.

    10ENTER1ENTER19+×2÷

You should see1: 100

RPN Power 48 key reference

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