[Music] hello kawamat in this video we define arithmetic sequence we also derive the formula for the nth term of an arithmetic sequence and given the first few terms of an arithmetic sequence we find the common difference in the n term for a sp specified n a sequence in which a constant d is called to be previous term to get the next term is called an arithmetic sequence the constant is called the common difference okay try nothing in first term the common difference and the next term in the given sequence halimbawa okay for the first sequence we have valentine two five eight and eleven sun in first term nothing jan so in first term nothing john is two then first number that's a given sequence next anonymous common difference the answer is three bucket so ropagnid is not in five ion2k5 that is three jung 5k8 that is also three young 8k 11 that is three so ebig surveying in common difference than given sequence i3 so next term uncommon difference okay 11. so therefore your next term nothing is 14. another example we have one one and one third one and two third two two and one third so a new first term not n so in first term nothing is one what is the common difference one third why so in my mind is nilang subtracting along in one and one third minus one parama uncommon difference another example we have seventeen twelve seven two and negative three so on in first term now then seventeen so anonymous common difference negative five twelve minus seventeen is negative five so therefore they took a negative three and negative five so the next term is negative eight nothing is five third term or young a sub three that is eight and then a sub four that is eleven let a sub one is equal to a sub 1 a sub 2 is equal to a sub 1 plus d and a sub 1 not n d by 2 plus the common difference that is 3 so therefore a sub 2 is equal to a sub 1 plus d and a sub 3 is equal to a sub 2 plus d so a sub 2 not n d bar a of the arithmetic sequence which is your a sub n is equal to the first term so your first term plus n minus 1 times the common difference okay so yanyong and term of an arithmetic sequence okay let's try to have an example find the 16th term of the sequence 1 five nine and thirteen so gamma the n term of arithmetic sequence so first identify muna natan yuma given so young first term nothing or a sub one nothing is one the uncommon difference is four bucket since nine minus five is equal to four or five minus one is equal to four and young n nothing is sixteen two numbers upon 16th term so gametyong minus 1 times difference nothing or your common difference is 4 and that is 16 minus 1 that is 15 so 1 plus 15 times 4 15 times 4 is 60 plus 1 so therefore the 16th term of the sequence is 61. okay next find the 20th term of the sequence we have 25 23 21 1917 again first even the gaga meeting formula so the first term i 25 young common difference a negative two why because 23 minus 25 is negative two and then young and nathan i 20 so hinahan so your a sub 1 is 25 plus n not n i 20 times the common difference which is negative 2. so subtract o 20 minus 1 is 19. times negative 2 that is negative 38 25 minus 38 that is negative 13. so therefore the 20th term of the sequence is negative 13. okay n term so find the nth term of the sequence 3 7 11 and 15. so panu native n term minus three the answer is four song in the hand up nothing is n term now so gamma two arithmetic sequence so it's a subtitle plus n minus one times four so only n terminal sequence so therefore it distributes n minus one so four times n four and yen and four times negative one that is negative four after that so pakistan like nothing younger one constant not end which is three and negative four so that is four n minus one see to you and terminal sequence nothing so next okay another example we have one five nine and thirteen so let a new first term not engine one common difference not in gen is four bucket four okay because five minus one is four so nothing young and term on it so again and a sub one nothing is one plus so distribute milan only four times n that is four n and four times negative one is negative three so combine similar terms sorry pakistan nothing on one minus four so one minus four is negative three so therefore young n term nothing is four n minus three in the sequence 50 45 40 35 which term is 5 so so the first term is 50 the common difference is negative 5 because 45 minus 50 is negative 5 so and then the a sub n is equal to 5 so not including s is equal to fifty plus n minus one times negative five so it took negative five nato you distribute nothing by n minus one so negative five times n can negative negative five n negative five times negative one that is positive five and then paksama nothing among common terms nothing yuma constant five fifty at the positive five so on gaga we not in libat not in c negative five ends so i'm again five n is equal to fifty plus five so it on five natalie but nothing negative five so five n is equal to 50 divide both sides by five paramagua nathaniel n so n is equal to ten so e big sub n young five diane 5 is the 10th term of or a sub 10 is equal to 5 okay in the sequence 7 10 13 16 which term is 43 a year a sub 1 is 7 the common difference is 3 why because 10 minus 7 is 3 and your a sub n is 43 so n term of arithmetic sequence 43 a sub 1 7 plus then distribution common difference n minus 1 3 times n that is 3n 3 times negative 1 that is negative 3. and then pakistan minority natin combine similar terms so c3n mali-lipatunsa left side so i am again negative 3n so 43 d but not in the right side so 7 minus 3 minus 43 that is negative 39 so divide both sides by negative 3 parabola so negative 39 divide negative 3 the answer is 13. 43 is the 13th term or the a sub 13 is equal to 43. okay for the next example the fourth term of an arithmetic sequence is 34 and the tenth term is 22. find a sub 1 the common difference and the n term since a sub 4 is 34 and a sub 10 is 22 so on gagavindang nathan six times six times the uncommon difference mulakai 34 so daddy get nothing and six times the common difference is 34 parama nothing in 22. so again in 34 9 is that is the fourth term and young 22 is the tenth term common difference so gamma king equation c34 six times the common difference para makuha nothing in 22 okay so not in detail common difference so the but nothing c34 is the right side 6d is equal to 22 minus 34 and that is 6d is equal to negative 12 and divide both sides by 6 therefore the common difference is negative 2. next to find a sub 1 subtract the common difference from a sub 4 three times since d should be subtracted the n minus 1 times prime a sub n in order to find the a sub 1 if it's a bean class okay bagu du mating a sub format long term no three times the common difference minus nothing a sub four parama not into a sub one so say a sub four that is 34. s three times the common difference from a sub 4. so 34 minus young and nothing is three okay this is four quesadilla fourth term no four minus one that is three times the common difference negative two so therefore 34 plus six bucket plus six negative three times negative two is positive six so a sub one nothing is forty last is the n term okay marina time common difference the negative two a sub one forty that is our first term and terminal arithmetic sequence formula which is 40 plus young and nothing times positive n times negative 2 that is negative 2 n negative 1 times negative 2 that is positive 2. therefore the nth term is negative 2 n plus 42 okay we're going to apply arithmetic sequence in real life situation consider this problem a company offers jeffrey's starting yearly salary of 240 000. with okay raises up twenty thousand pesos per year what will be your salary on the tenth year so bawata own again christian saudi jeffrey and twenty thousand so young starting salary is 240 000. 10th year okay so since your first salary yeah so that is our first term no 000 and then terminating so that is 10 and then the common difference is 20 thousand bucket increasing every year so gamete formula subtitling nothing i'm a given value so 240 000 plus 10 minus one that is nine times twenty thousand so two hundred forty thousand plus nine times twenty thousand the answer is four hundred twenty thousand so this is the salary now me jeffrey back the thing tenth year thank you for watching this video i hope you learned something don't forget to like subscribe and hit the bell button but updated ko for more video tutorial this is your guide in learning your mod lesson your walmart channel