Ppt x-ruby(revised)
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Transcript of Ppt x-ruby(revised)
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ArithmeticSequence
Featuring: A Dilemma of Derpina
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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
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Mae’s Dilemma
Can you help me with my reviewing schedule??!!
YES No
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Mae’s Dilemma
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Mae’s Dilemma
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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
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Mae’s Dilemma
Well Thank you for helping! So now let’s start on making the
schedule.
CLICK ME!!
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Mae’s Dilemma
Are you ready to
discuss my recommended review
schedule for you?
Yes! Ma’am
Not now!
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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
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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
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Mae’s Dilemma
WHAT!!!!! WOULDN’T THAT BE SO LONG!!! HOW LONG WILL IT
BE FOR THE FIRST WEEK?
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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
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Mae’s Dilemma
Well there’s a sequence that can be used do you
know what is it?
Yes No
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What is it then?
Harmonic Sequence
Geometric
Arithmetic
Fibonacci
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NO!
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Mae’s Dilemma
Correct! Now before we start off I would like to
discuss some things about arithmetic Sequence
Okay let’s proceed then
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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
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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
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Do you think you can solve our problem now?
Yes No
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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
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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?
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Mae’s Dilemma
Now with the enough information we have we
may now start solving the problem
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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
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Mae’s Dillema
Okay, now that we have acquired everything that
we will need for solving the problem let’s now proceed
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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
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Mae’s Dilemma
Good Job! Now that we know the answer let’s go and tell
Derpina the result
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Mae’s Dilemma
Derpina! We’re done solving the question the
total time to be consumed for the review is about 5 ¼
hours….
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Mae’s Dilemma
O.M.G ! Thank you ma’am now I can start my review session with the review schedule you
gave me!
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~~~THE END~~~~Prepared by: Gabriel Fetalvero Section:RubySubmitted to: Sir. Eric De Guzman