Finding the formula for a sequence of terms

👉 Learn how to write the rule of a sequence given a sequence of numbers. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence.

To write the explicit formula of a sequence of numbers, we first determine whether each term of the sequence is obtained by adding/subtracting a common value to the preceding term or whether each term of the sequence is obtained by multiplying a pre-determined value, called the common ratio, to the preceding term or neither.

For the first case, the sequence is an arithmetic sequence and we can write the explicit formula by plugging the common difference into the arithmetic sequence explicit formula. For the second case, the sequence is a geometric sequence and we can write the explicit formula by plugging the common ratio into the geometric sequence explicit formula. For the third case, we can examine the pattern and by some kind of trial and error, we can be able to write the explicit formula.

Organized Videos:
✅ Sequences
✅Sequences | Learn About
✅Determine The First Five Terms of The Arithmetic Sequence
✅How to Write The Formula for a Arithmetic Sequence
✅Find the nth Term of an Arithmetic Sequence
✅Find the First Five Terms of a Geometric Sequence
✅How to Write The Formula for a Geometric Sequence
✅Find the nth Term of a Geometric Sequence
✅How to Determine Arithmetic or Geometric Sequence
✅Find the First Five Terms of a Sequence
✅How to Write The Formula for a Sequence
✅Find the nth Term of a Sequence
✅How to Simplify Factorials
✅Recursive Sequences
✅Prove the Sum by Induction
✅Find the Given Term of Binomial Expansion
✅Binomial Expansion | Learn About
✅How to Expand a Binomial

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#sequences #brianmclogan

[mohamadelharakeh]

this will be my last video of this semester . thank you so much for all the work you put in your videos .. you were more helpful than the teacher i paid to be .. again thanks so much for every video you did.

[jiiskookonly]

If we only have a teacher like that in which we can ask freely if we have question😢

[charisegumapac]

I really love your videos. All the lessons that I can't understand makes sense now after watvhing yours. Thank God I have someone to learn more from!Thanks Brian💗
-from Philippines

[spooksmeister]

Thank you Mr. Logan! I have always looked to you for help since 2 years!

[lolliz]

That last question that student asked at the end was my concern as well.... Which is: Is there another way of figuring out the Formula other than trying arbitrary methods until it works. Lol.

I was hoping that the general format of Arithmetic Progression or Geometric Progression would always easily manifest the formula, but after watching many videos, I've seen that what you all have in common is just trying different operations and mix of operations until it gives rise to the progressing terms. So I guess I can conclude that's the nature and approach of the topic Sequences & Series.
But this was nicely reasoned out though, Thankyou.

[ankitbhandari]

Thank you for yrs valuable information sir .keep it up.

[thisrandomdude_]

Woah. Mind blown. This was so interesting to learn! I'm sure it'll come in handy next year, when we deelve deeper into arithmetic series.

[yourfavlightskin]

The love i have for this teacher I hope he is my algebra 2 teacher I bet he would be the smartest teacher in our school 😂

[YimengandCharles]

wow the patience you have with those questions I would lose it

[conordonovan]

This dude is awesome, serious math teacher vibes too haha

[megsalex]

What about this problem... Gregor has decided to create a new sequence that starts with the numbers 4, 1, 5, 6, 11, ... where each term after the first two terms is found by adding the two previous terms. On the 25th term, his addition was off by . That is, the sum was 1 greater than the correct one. If he made no other mistakes, how far off was the 35th term?
Term 1 = 4Term 2 = 1Term 3 = Term 1 + Term 2 = 4 + 1 = 5Term 4 = Term 2 + Term 3 = 1 + 5 = 6Term 5 = Term 3 + Term 4 = 5 + 6 = 11
Thank you so much if u can help I’m just so confused I don’t know at all what to do

[ed]

Really good inductive approach. Thank you for uploading

[carlik]

How do I find an when the sequence is increasing by a power? 18, 20, 24, 32, 48

[notsurewhattoputhereyet]

whoever kept interrupting him was really annoying.

[jeanroseromo]

What if sir Everything is positive but the same term that u give?

[Dr.PayalHiranwar]

I like your way of teaching. Mine is also the same. I like students asking me doubts in the class. It's only then that their concepts get cleared. I am from India 🇮🇳. You are doing great Job👌

[VijaySingh-bhgo]

How do you find the quadratic sequence with only the 2nd term and 4th term to

[xyfinedaydreamer]

You enlightened my mind thank you much😊👍

[alrayhankamal]

Can someone tell me the meaning of the (-1)^n? Pls?

[professorthanos]

How can I find the answer to 1, -4, 9, -16, 25? I kinda understand the video but how can i find the explicit formula to the question above?