ArithmeticSequence

Featuring: A Dilemma of Derpina

Derpina consulted her teacher about her daily review schedule due to her time management problem . Her teacher suggested that she must start with a 30 minute review in the first day and add 5 minutes for the proceeding days. How many minutes will Derpina consume in total for the first week?

Situation

Mae’s Dilemma

Can you help me with my reviewing schedule??!!

YES No

Mae’s Dilemma

Mae’s Dilemma

Mae’s Dilemma

Hi Good Day! I am Derpina’s teacher, I am helping her on making a review schedule can you

help me?

No

Yes

Mae’s Dilemma

Well Thank you for helping! So now let’s start on making the

schedule.

CLICK ME!!

Mae’s Dilemma

Are you ready to

discuss my recommended review

schedule for you?

Yes! Ma’am

Not now!

Mae’s Dilemma

Well the easiest way for you to overcome your problem is by having a review schedule. Well i

would like to recommend you some schedule but

you’re going to need some math to get it . Are you

ready for it?

Yes

No

Mae’s Dilemma

How about if you start with a 30 minute review in the first day and add 5 minutes for the proceeding

days? Wouldn’t that be easier?

Yes No

Mae’s Dilemma

WHAT!!!!! WOULDN’T THAT BE SO LONG!!! HOW LONG WILL IT

BE FOR THE FIRST WEEK?

JUST DO IT!!!!

Well if you want to get your review schedule right you’d better make one

now go get back from the start

Mae’s Dilemma

Well there’s a sequence that can be used do you

know what is it?

Yes No

What is it then?

Harmonic Sequence

Geometric

Arithmetic

Fibonacci

NO!

Mae’s Dilemma

Correct! Now before we start off I would like to

discuss some things about arithmetic Sequence

Okay let’s proceed then

Can be Written in the form of “a₁ , a₁+d ,a₁+2d…..

Arithmetic Sequence can be obtained by adding a constant called Common Difference.

a₁ is the first term of an Arithmetic sequence d is the common difference an is the unknown term In order to find a unknown term we could use

this formula an = a₁+(n-1)d

Arithmetic Sequence

There’s a formula for that. The formula is Sn=n/2(a₁+an)

Sn is the sum of terms N is the nth term a₁ is the first term an is the last term

Solving for the sum of terms

Do you think you can solve our problem now?

Yes No

Mae’s Dilemma

So now in order for us to have a clearer

understanding let’s make an example of solving a

undefined term in a Arithmetic Sequence

3,4,5,6,7, _ Now let’s use the formula given awhile

back. an = a₁ +(n-1)d a₁ = 3 d=1 n=6 a6= 3+(6-1)1

a6=8

What is the nth term of the sequence below?

Mae’s Dilemma

Now with the enough information we have we

may now start solving the problem

Given: a₁= 30, d=5, n=7 Required: a7=?

Equation: an = a₁+(n-1)d Solution: a7 = 30+(7-1)5 a7 = 30+30 Answer : a7=60

Solving the problem

Mae’s Dillema

Okay, now that we have acquired everything that

we will need for solving the problem let’s now proceed

Given: a₁= 30, d=5, n=7, a7=60

Required: Sn=? Equation: Sn=n/2(a₁+an)

Solution: Sn=7/2(30+60)

Sn=7/2(90)

Sn=630/2 or 315 minutes Answer: 315 minutes or 5 ¼ hours

Solving for the sum of terms

Mae’s Dilemma

Good Job! Now that we know the answer let’s go and tell

Derpina the result

Mae’s Dilemma

Derpina! We’re done solving the question the

total time to be consumed for the review is about 5 ¼

hours….

Mae’s Dilemma

O.M.G ! Thank you ma’am now I can start my review session with the review schedule you

gave me!

~~~THE END~~~~Prepared by: Gabriel Fetalvero Section:RubySubmitted to: Sir. Eric De Guzman