Calculator Technique for Geometric Progression

Calculator Technique for Geometric Progression

To solve for n, AC → 9565938 SHIFT → 1[STAT] → 7:Reg → 4:x-caret 9565938x-caret = 15

Problem Given the sequence 2, 6, 18, 54, ...

answer

Sum of the first ten terms,

1. Find the 12th term

AC → SHIFT → log[Σ] → ALPHA → )[X] → SHIFT → 1[STAT] → 7:Reg → 5:y-

2. Find n if an = 9,565,938.

caret → SHIFT → )[,] → 1 → SHIFT → )[,] → 10 → )

3. Find the sum of the first ten terms The calculator will display Σ(Xy-caret,1,10) then press [=].

Solution by Calculator

Σ(Xy-caret,1,10) = 59048 ← answer

Why A·B^X? The nth term formula an = a1rn – 1 for geometric progression is exponential

You may also sove the sum outside the STAT mode

in form, the variable n in the formula is the X equivalent in the calculator.

(MODE → 1:COMP then SHIFT → log[Σ])

MODE → 3:STAT → 6:A·B^X X

Y

1

2

2

6

3

18

Each term which is given by an = a1rn – 1. $\displaystyle \sum_{x=1}^{10}$(2(3ALPHA X - 1)) = 59048

Or you may do $\displaystyle \sum_{x=0}^{9}$(2 × 3ALPHA X) = 59048

To solve for the 12th term AC → 12 SHIFT → 1[STAT] → 7:Reg → 5:y-caret 12y-caret = 354294

answer

1

answer

Calculator Technique for Harmonic Progression

3. Find the 52nd term. 4. If the nth term is 250, find n.

Problem

5. Calculate the sum of the first 60 terms.

Find the 30th term of the sequence 6, 3, 2, ...

6. Compute for the sum between 12th and 37th terms, inclusive. Solution by Calculator Among the many STAT type, why A+BX?

MODE → 3:STAT → 8:1/X X

Y

1

6

2

3

3

2

The formula an = am + (n - m)d is linear in n. In calculator, we input n at X column and an at Y column. Thus our X is linear representing the variable n in the formula. Bring your calculator to Linear Regression in STAT mode: MODE → 3:STAT → 2:A+BX and input the coordinates. X (for n)

Y (for an)

6

12

AC → 30 SHIFT → 1[STAT] → 7:Reg → 5:y-caret

30

180

30y-caret = 0.2

To find the first term:

answer

AC → 1 SHIFT → 1[STAT] → 7:Reg → 5:y-caret and calculate 1y-caret, be sure to place 1 in front of y-caret.

Calculator Technique for Arithmetic Progression

1y-caret = -23 → answer for the first term

To find the 52nd term, and again AC → 52 SHIFT → 1[STAT] → 7:Reg → 5:yProblem: Arithmetic Progression The 6th term of an arithmetic progression is 12 and the 30th term is 180.

caret and make sure you place 52 in front of y-caret. 52y-caret = 334 → answer for the 52nd term

1. What is the common difference of the sequence? 2. Determine the first term?

2

To find n for an = 250,

Another way to solve for the sum is to use the Σ calculation outside the STAT mode.

AC → 250 SHIFT → 1[STAT] → 7:Reg → 4:x-caret

The concept is to add each term in the progression. Any term in the progression is given by an = a1 + (n - 1)d. In this problem, a1 = -23 and d = 7, thus, our equation for

250x-caret = 40 → answer for n

an is an = -23 + (n - 1)(7).

To find the common difference, solve for any term adjacent to a given term, say 7th

Reset your calculator into general calculation mode: MODE → 1:COMP then SHIFT

term because the 6th term is given then do 7y-caret - 12 = 7 for d. For some fun,

→ log.

randomly subtract any two adjacent terms like 18y-caret - 17y-caret, etc. Try it!

Sum of first 60 terms: $\displaystyle \sum_{x=1}^{60}$ (-23 + (ALPHA X - 1) × 7) = 11010

Sum of Arithmetic Progression by Calculator Sum of the first 60 terms: AC → SHIFT → log[Σ] → ALPHA → )[X] → SHIFT → 1[STAT] → 7:Reg → 5:y-

Or you can do

caret → SHIFT → )[,] → 1 → SHIFT → )[,] → 60 → )

$\displaystyle \sum_{x=0}^{59}$ (-23 + 7 ALPHA X) = 11010 which yield the same result.

The calculator will display Σ(Xy-caret,1,60) then press [=]. Σ(Xy-caret,1,60) = 11010 ← answer

Sum from 12th to 37th terms $\displaystyle \sum_{x={12}}^{37}$ (-23 + (ALPHA X - 1) × 7) = 3679

Sum from 12th to 37th terms, Σ(Xy-caret,12,37) = 3679 ← answer

Or you may do $\displaystyle \sum_{x=11}^{36}$ (-23 + 7 ALPHA X) = 3679

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