[Music] hi Monica wama in this video we will define sequence finite and infinite sequence we will list the next few terms given several consecutive terms of a sequence and we will derive a mathematical expression or rule for generating the sequence by pattern searching let's have person activity song gaga be met in a laminate in common among us also not know letters or numbers okay so for number one I have a B G and J so I know how are you - also not know letters we have M p s what is the pattern we will skip two letters next for number two I have 1 3 5 7 what is the pattern this are numbers that are odd so therefore what's next for 7 we have 9 11 and 13 for number 3 we have 1 4 9 16 and 25 what are these numbers or what do you think is the pattern so these numbers are all perfect squares so what is next to 25 we have 36 49 and 64 number 4 we have 5 15 25 and 35 what do you think are the next numbers so we have 45 55 and 65 what is the pattern we will just add 10 from the previous number so 5 plus 10 15 plus 10 25 plus 10 five plus ten forty five and so on and so forth and then point number five we have one three six ten we have fifteen twenty one and twenty eight what is the pattern we will add two from 1 so 1 plus 2 that is 3 3 plus 4 that is 6 6 plus 4 we have 10 so therefore we will add 5 to 10 and that makes it 15 and then plus 6 21 plus 7 28 so human Anette not n plus 2 Plus 3 plus 4 plus 5 6 consecutive numbers ok so a sequence is a function whose domain is the set of positive integers it also means an ordered list of numbers we have two kinds of sequences as sequences infinite if its domain is the set of positive integers without a last term so kapag me Nikita I am three dots or ellipsis young on Maxis Ibiza attend that the sequence is infinite while a sequence is finite if its domain is the set of positive integers which has a last term or sometimes it is represented by n so Huma poppins enumeration last term that is a finite sequence now each number in a sequence is called the term and the ban term halimbawa I have five ten I know 5 15 25 35 and 45 so poxy nominating term at AU first term second term third term fourth term and fifth term so how many terms do we have we have five terms now remember that your end rep is represented by the order young n opinion i order noon terms not an indian you miss mom number Nagila like a nothing I am 5 15 25 35 and 45 Hindi yon it's the order it's one two three four five in the sequence 1 3 6 10 15 we can denote that the terms as follows so a sub 1 u 1 a tour that is first term so what is our first term that is 1 a sub 2 means a sub 2 second term that is 3 a sub 3 that is your third term so that is 6 is a 4 is 10 and E sub 5 is 15 shyam parliament termed entire sequence now what if in animal what is that 28 term what is the 19th term so panel not in saponin Gentile Kagame tanam general term orient in atomic nothing rule so at all time that general term net or role at am wedding at intermittent param maha Hinata new manga Susan Edna terms la Luna NASA mulana Silla so let us prove first school Tama bottom rule NATO so halimbawa I have a sub 1 so a sub 1 means first term in Manhattan boom telegin and NASA first term I 1 using this rule so 1 is equal to 1/2 and then we would add this 1 plus 1 so that will become 2 so you may cross out or cancel so - and that makes it 1 so 1 times 1 that is 1 so our first term a sub 1 is equal to 1 which is correct next a sub 3 means our three terms so we will substitute again 3 to all of the end variables so we have a sub 3 is equal to from n over e to that will become 3 over 2 and then n plus 1 that will become 3 times 3 plus 1 because we are referring to destroy it term okay so we have add 3 plus 1 that will become 4 and then 4 divide 2 that makes it - two times three is six for a raise to 5 so Aries - five fifth term let's check if it's really 15 so substitute five to all n so we have e sub 5 is equal to 5 over 2 for n - over 2 and then 5 plus 1 for n plus 1 so we will add 5 plus 1 that will become 6 whether in among mag multiplay communi 5 times 630 divided 2 that is 15 or padding 6 divided 2 Marco Castillo that is 3 3 times 5 that is still 15 for a sub 2 we have in second term so to D by of divide 2 times the quantity of 2 + 1 equals 3 let's see 2 plus 1 is 3 3 times 2 is 6 divided 2 that is 3 so our second term now is 3 and that is correct and an e sub 4 we have 4 over 2 times the quantity of 4 plus 1 4 plus 1 that is 5 times 4 20 divided 2 is 10 and a sub 4 is equal to then okay so find the first five terms of the sequence whose general term is given by a sub n is equal to the quantity of n - 3 raise to n so Tito who need not in your first 5 terms so you own and among terms and if I iron so Bennigan's general term let's try to solve so given your formula or rule not a sub n is equal to the quantity of n - 3 raise to n so max a substitute I own am one the ones among n since I'm gonna hang up not in a first term so first term aquinnah hang up on me like a nothing's among n million I won so let us solve 1 - 3 that will become negative 2 and negative 2 raised to 1 is negative 2 that will be our first term next first the our second term so since second naina hang up nothing is a substitute nothing and two's among n so we have now two minus three that is negative 1 and negative 1 raise to 2 that is 1 so since negative 1 times negative 1 same sign that will become positive 1 next pour the third term we are looking for the 3 term so we will substitute 3 semana n so 3 minus 3 that is 0 and 0 raise to 3 is 0 for our fourth term we have 4 minus 3 that is 1 and 1 raise to 4 is positive 1 and for our fifth term so we have 5 minus 3 that is 2 & 2 days 2 5 is 32 so we now have the first 5 terms of the general term a sub n is equal to the quantity of n minus 3 raise to n we have negative 2 1 0 1 and 32 next find the first four terms and that 20th term of the sequence whose general term is given by a sub n is equal to the quantity of negative 1 raised to n over 2 n minus 1 so 809 seen as abiko we really need the general term or usual nothing can say make a Cessna Punk 20th term young teen Anton own so pan and not in some economist maybe less with the help of the general term so that's all so for the first term so I'm gonna nothing I go in substitute nothing new one selahattin hang in ayan Shire so we now have a negative 1 raised to one that is still negative 1 and then substitute 1 to 2 n so we have 2 times 1 that is 2 minus 1 that is 1 so negative 1 over 1 that is negative 1 for our second term substitute substitute 202 all of our n so we now have 1/3 for our third term subs we will substitute 3 so we have negative 1 raised to 3 that makes it negative 1 and then 2 times 3 is 6 6 minus 1 that is 5 so we will now have negative 1 pip next for our fourth term so substitute for 2n so negative 1 raise to 4 that is positive 1 now remember if our exponent is an even number the product is positive but if our exponent is an odd number the product is negative and then let's go back 2 times 4 that is 8 8 minus 1 that is 7 so we now have 1 over 7 now let's find out that 28 term a so that 28 term we will substitute 20 so negative 1 raised to 20 since 20 is an even number therefore the product is positive 1 and then 2 times 20 that is 40 minus 1 is 39 so the 20th term is 1 over 39 now remember that if you have the quantity of negative 1 raised to n this is the general term that causes the science of the terms to alternate between positive and negative so photography turnitin to negative 1 raised to n enm palette and an Athena um terms nothing I Maggie Ginn alternate and science a guy Anita example Natoma poppin senior negative positive negative positive what is it positive because since 2008 therm Shire Huma Poppins in your latyout second term Natan at 4th term I even numbers also 20 so ibig sabihin lahat Manasa even number not in the term I positive okay now but achter de montejo so given a sequence we will find out the general term or the rule so I have here one 827 64 and 125 what do you think is the general term Hey so all of these numbers are the cube of the numbers so this will become a sub n is equal to n raise to 3 and in bagua 1 1 raise to 3 is 1 times 1 1 times 1 that is still 1 and then 2 2 times 2 4 times 2 that is 8 that's why it's n raised asleep next I have one 1/2 1/3 it's 1/4 1/5 so what do you think is the general term ok come up happens in your the denominators just increase consecutively so knock in increased lung Shan oh macha passionate vaccine IV not in consecutive kappa so annoyed okay so therefore the general term is e sub n is equal to 1 over n whom I know you term yeah company long-term share that is the denominator Thanks I have negative 5 10 negative 15 20 and negative 25 so what is that general term Sakuma POPPINS is not an item on the numbers net oh i multiples of 5 now they know come up happens in a tent and same Cienega alternate so I know my is in attica Vanina and a gamete in Kappa Gong science not in ienaga alternate we will use the quantity of negative 1 raised to n now since multi-position and 5/8 times lung that interest of 5 n next I have 1 4 9 and 25 so the general turn is what are these numbers these are all perfect squares so therefore our general term is a sub n is equal to n raised to 2 next I have 3 negative 6 9 negative 12 and 15 what is the general term so nagas alternate 9 dementia so we will be using negative 1 raised to n minus 3 n okay thank you for watching this video I hope you learned something don't forget to Like subscribe and hit the bell button so our Walmart channel just keep on watching