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tor Techniques for Solving Progression Problems

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Glossary

## Popular

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

## The following models of CASIO calculator may work with these methods: fx-570ES,

• 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

# But before that,

note the following calculator keys and the corresponding operation: Name

SHIFT → CALC

Logical equals

# Exponent

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

# What is the common difference of the sequence

## Determine the first term

### Find the 52nd term

If the nth term is 250,

# Compute for the sum between 12th and 37th terms,

• inclusive

the traditional way of solving this problem is presented here

• → common difference

## Operation

• → 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

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

### Among the many STATtype,

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

X (for n)

## Y (for an)

• calculator,

we input n at X column and an at Y column

#### Thus our X is linear representing the variable n in the formula

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

### To find n for an = 250,

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

## To find the common difference,

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

### For some fun,

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

## Why MODE → 3:STAT → 3:_+cX2

? 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

#### Sum from 12th to 37th terms,

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

## In this problem,

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

-23 + (n

- 1)(7)

# Reset your calculator into general calculation mode: MODE → 1:COMPthen SHIFT → log

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

• - 1) × 7)= 11010

## Sum from 12th to 37th terms (-23 + (ALPHA X

• - 1) × 7)= 3679

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

### Find the sum of the first ten terms

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

Why A·B^X

## X 1 2 3

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

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

#### AC → 9565938 SHIFT → 1[STAT] → 7:Reg → 4:x-caret 9565938x-caret= 15

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

# X 1 2 3

### Y 6 3 2

#### AC → 30 SHIFT → 1[STAT] → 7:Reg → 5:y-caret 30y-caret= 0

I hope you find this post helpful

# With some practice,

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

## I encourage you to do some practice,

• once you grasp it,

you can easily solve basic problems in progression

## If you have another way of using your calculator for solving progression problems,

• please share it to us

We will be happy to have variety of ways posted here

### You can use the comment form below to do it

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

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