[Music] in previous lesson you already know sequences in which a certain number is added to each term to get the next term now you will explore sequences in which a certain number is multiplied so in this video we define geometric sequence and also we identify the common ratio in the next term of the sequence find the n term of the geometric sequence and solve problems involving geometric sequence we're going to understand how to use to get the ratio to the concept of ratio for this type of sequence so let's have a short activity find the ratio of the second number to the first number for your example number one we have two and eight song enumeration in dalawa individual second number this is the first number so that will be eight divide two so therefore young raising ends is four for number two we have negative three and nine so divide like nothing young nine k negative three so generation into a negative three for number three we have one and one half so if you divide that lattice one half k one so the ratio is one half a sequence is geometric if there exists a number r called the common ratio so we are the uh we represent common ratio letter uh the small letter r the common ratio r can be determined by dividing any term in the sequence by the term that precedes it okay let's have an example identify the common ratio and the next term in the following sequences for number one we have one two four and eight of course kanina is the first activity nathan a diniscus so therefore not young next term emo multiplayer tends to eight imo multiply not n c two k eight parama young next term so the next term is 16 since eight times two is equal to sixteen for number two we have eighty twenty and five same process parama are not in uncommon term so 20 over 80 that is one-fourth so parama young next term imma multiply nothing five one-fourth so that is the next term is five over four since five times one fourth so that is five times one is equal to five all over four okay for number three we have two negative 8 32 and negative 128 same process to get the common ratio they divide long nothing in second terms uh first term so that is negative 8 over 2 that is equal to negative four so therefore your next term nothing immo multiply nothing's negative 128 k negative four and that is five hundred twelve okay you all know that the geometric sequence sequence the geometry my common racist so i'll give you more examples to identify the given sequences if this sequence is geometric or not okay i have four examples here so for the first example we have 5 20 80 twenty of course but universe nothing in 20k pipe and the answer is four young 80 divided k20 the answer also is four okay 320 divided by 80. the answer is also four so so therefore meron silang common ratio so this is a geometric sequence another seven square root of two five square root of two three square root of two and square root of two so to check pagini write not tension five square root of two by seven square root of two omega one nothing is five over seven because nothing c three square root of two page is not a geometric sequence for number 3 we have 5 negative 10 20 and negative 40. so same process divide nothing in second terms of first term so to check for my common ratio negative 10 divide 5 that is negative 2 20 divided by negative 10 the answer is negative 2. at your negative 40 divided 20 the answer also is negative two so therefore marrow is uncommon ratio so in number three not ten is a geometric sequence for number four we have ten over three ten over six ten over nine and ten over fifteen so checking muna natan kumai common ratio given sequence so apparently nothing in second terms of first term is one half ten over nine over ten over six and so i got a two third and ten over fifteen over ten over nine and sagot i three fifth so mag so therefore number four is not a geometric sequence the n term of a geometric sequence is given by a sub n so tandem for millennia is equal to a sub 1 times r raised to n minus 1. take note r should not be equal to zero so young a sub one nothing d though that is our first term and young are not then is young common ratio net n young n that is the number of terms okay okay let's try to answer this example what is the tenth term of the geometric sequence given eight four two and one so identify muna natin yuma given so your common relation at n so four over eight that is one half your first term nothing that is eight so we're using this formula so on gagawi ng nathan is okay so a sub 1 that is 8 times 1 half raised to ten minus one back at ten so we have ten terms and not ten and then eight times one half so ten minus one is nine then one half raised to nine so on gagavin okay so that is one half raised to nine so that is one times raised to negative one two raised to nine is five hundred twelve and then multiply that is eight over five hundred twelve and then eight over five hundred twelve is massive so that is the final answer is one over 64. okay so madali lang using the formula so i have here another set of uh activity or exercises find the missing term in three twelve forty eight so on gaga in munich and of course nathan and that is 48 times 4 that is 192. so i'm consumed at 192. so you concentrate 192. same process times k4 so the answer is 768. another find the missing term in okay blank flank 32 64 128. and then 16 divide two that is eight so in first term this is eight and young 16. okay i have here uh one problem okay where in the geometric sequence nah pedinating apply during the initial pace of an outbreak of missiles the number of infection can grow geometrically if there were 4 8 16 on the first three days of an outbreak of the missiles how many will be infected on the sixth day okay gamete formula that is two and then your first term nothing is four and then young and nothing is six so gamma in formula substitute the value the first term is 4 and then this is the common ratio raised to 6 minus 1 and then 4 times 2 raised to 5 and 2 raised to 5 is 32 32 times four that is 128 ebx a bn there will be 128 people in infected with measles on the sixth day thank you for watching this video i hope you learned something don't forget to like subscribe and hit the bell button put updated ko for more video tutorial this is your guide in learning your math lesson your walmart channel