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tor Techniques for Solving Progression Problems





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

Using it will save you plenty of time and use that time in analyzing more complex problems

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

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


Σ (Sigma)

SHIFT → log


Logical equals




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,

Calculate the sum of the first 60 terms

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

Traditional Solution For a little background about Arithmetic Progression,

the traditional way of solving this problem is presented here

Click here to show or hide the solution


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

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,

X (for n)

Y (for an)

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


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

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,

Input three coordinates X 1 2 3


Sum of the first 60 terms: (AC → 60 SHIFT → 1[STAT] → 7:Reg → 6:y-caret) 60y-caret= 11010

Why MODE → 3:STAT → 3:_+cX2

? The formula S = ½n[ 2a1 + (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

The concept is to add each term in the progression

Any term in the progression is given by an = a1 + (n

In this problem,

-23 + (n

- 1)(7)

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

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

Or you can do (-23 + 7 ALPHA X)= 11010 which yield the same result

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

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

Calculator Technique for Geometric Progression Problem Given the sequence 2,

Find the 12th term 2

Find n if an = 9,565,938

Find the sum of the first ten terms

Traditional Solution Click here to show or hide the solution

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

To solve for n,

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

Or you may do (2 × 3ALPHA X)= 59048

Calculator Technique for Harmonic Progression

Problem Find the 30th term of the sequence 6,

Solution by Calculator MODE → 3:STAT → 8:1/X

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,

you can easily solve basic problems in progression

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

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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