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tor Techniques for Solving Progression Problems

Description

Glossary

Calculator Techniques for Solving Progression Problems

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This is the first round for series of posts about optimizing the use of calculator in solving math problems

The calculator techniques I am presenting here has been known to many students who are about to take the engineering board exam

- fx-570ES Plus,
- fx-115ES,
- fx-115ES Plus,
- fx-991ES,
- and fx-991ES Plus

This post will focus on progression progression

To illustrate the use of calculator,

we will have sample problems to solve

note the following calculator keys and the corresponding operation: Name

SHIFT → CALC

Logical equals

Problem: Arithmetic Progression The 6th term of an arithmetic progression is 12 and the 30th term is 180

If the nth term is 250,

- inclusive

the traditional way of solving this problem is presented here

- → common difference

- → first term
- → 52nd term
- → 40th term,
- a40 = 250 Sum of AP is given by the formula

Sum of the first 60 terms → answer Sum between 12th and 37th terms,

- inclusive
- → answer

Calculator Technique for Arithmetic Progression Bring your calculator to Linear Regression in STAT mode: MODE → 3:STAT → 2:A+BXand input the coordinates

- why A+BX
- ? The formula an = am + (n
- - m)d is linear in n

X (for n)

- calculator,

we input n at X column and an at Y column

To find the first term: AC → 1 SHIFT → 1[STAT] → 7:Reg → 5:y-caretand calculate 1y-caret,

be sure to place 1 in front of y-caret

1y-caret=

- → answer for the first term

To find the 52nd term,

and again AC → 52 SHIFT → 1[STAT] → 7:Reg → 5:y-caretand make sure you place 52 in front of y-caret

- 52y-caret= 334
- → answer for the 52nd term

AC → 250 SHIFT → 1[STAT] → 7:Reg → 4:x-caret 250x-caret= 40

- → answer for n

solve for any term adjacent to a given term,

say 7th term because the 6th term is given then do 7y-caret- 12 = 7 for d

randomly subtract any two adjacent terms like 18y-caret- 17y-caret,

! Sum of Arithmetic Progression by Calculator Bring the your calculator to Quadratic Regression in STAT mode MODE → 3:STAT → 3:_+cX2

Note that for the given AP,

- and a3 =

Input three coordinates X 1 2 3

-23-16-9

? The formula S = ½n[ 2a1 + (n

- - 1)d ] for sum of arithmetic progression is quadratic in n

In our calculator,

we input n in the X column and the sum at the Y column

use SHIFT → 1[STAT] → 7:Reg → 6:y-carettwice 37y-caret

- - 11y-caret= 3679 Another way to solve for the sum is to use the Σ calculation

- -23 and d'= 7,
- our equation for an is an =

-23 + (n

- 1)(7)

Sum of first 60 terms: (-23 + (ALPHA X

- - 1) × 7)= 11010

- - 1) × 7)= 3679

Or you may do (-23 + 7 ALPHA X)= 3679

Traditional Solution Click here to show or hide the solution

Solution by Calculator MODE → 3:STAT → 6:A·B^X

Why A·B^X

The nth term formula an = a1rn – 1 for geometric progression is exponential in form,

the variable n in the formula is the X equivalent in the calculator

Y 2 6 18

Sum of the first ten terms (MODE → 1:COMPthen SHIFT → log) Each term which is given by an = a1rn – 1

- (2(3ALPHA X
- - 1))= 59048

I hope you find this post helpful

you will get familiar with your calculator and the methods we present here

- once you grasp it,

you can easily solve basic problems in progression

- please share it to us

We will be happy to have variety of ways posted here

Tags: scientific calculatorcalculator techniqueCASIO calculatorarithmetic progression by calculatorgeometric progression by calculatorharmonic progression by calculator

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