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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