sequences-and-series-al2-finding-nth-term-common-difference-explicit-formula

# Interactive video lesson plan for: Sequences and series al2 finding nth term common difference explicit formula

#### Activity overview:

For more cool math videos visit my site at http://mathgotserved.com or http://youtube.com/mathsgotserved Good day students in this clip were going to be going over an example on finding arithmetic sequence is of finding the

common difference to end term and the explicit formula of terms of an arithmetic sequence so let's take a look at the of

instructions for the examples the sport the given sequence determine if it is an arithmetic or geometric sequence find the

common difference for racial find the next three terms of the sequence find the value of a thirty and lastly, find the

explicit formula is it to verify your answer indeed. Right let's take a look at thus sequence under consideration for

number one we of fourteen four negative six and negative sixty in in the sequence continues okay of the difference between

sequence a series is the elements of of the terms in a sequence are separated by commas present a series you have plus or

minus is between them. Okay so think of sequence against a list of numbers were asked to misuse represents the Psalm of of

numbers okay right so am part payment to determine if it's arithmetic or geometric. So when is negative arithmetic

registered a side note here arithmetic we have a common difference, and difference for arithmetic unit is repeated

addition or subtraction that's how subsequent terms of the sequence are generated on the other hand for geometric you have

a common ratio okay, one graciously constantly multiply to generate of the next terms of the geometric sequence to think

of this as pattern subtract and this would think of it as multiply and divide right so determine if his arithmetic or

geometric the going to see if our differences the ratio it will, and difference or the common ratio okay so let us start

with arithmetic tests first for arithmetic series to go a different D has to be equal to of eight two minus eighty-one

asked to be equal to the three minus eight two and has equal to a four minus eight three and out pattern have to continue

basically the formula for, differences a seven and a term minus the term before it is how you guessed it, and difference

team is get the same number every single time. Right let's look at the series in this case of this is a one the first time

the index tells you the position okay from a one and is the last terms to that's a one and a half eight two and this is a

three in this term have right here is a four okay so let's use the services see if we're having a common difference here

okay if it's not a common difference that this is not an arithmetic sequence right is apply the formula eight two minus

eighty-one eighty minus eighty-one cases for minus eighty-one is fourteen okay and then what is of this coming what is

this cannot to four minus fourteen is negative ten right let's try a three minus eight two eight three is negative six

minus eight to negative four. The computer difference have negative ten looking get a four minus eight three A4 is

negative sixteen minus of negative six we it becomes negative sixteen plus sixty go/-- these two basic into six three to

number negative be subtract and keep the number of the the sign of the bigger number so this is negative ten also what is

the about this three numbers the constantly the same so this means that this is an arithmetic sequence this is an

arithmetic sequence sequence line of because we have a common difference okay because there is a common difference there

is a common difference right of another way to look at it is look at the pattern of numbers right here from 10 to 4

subtract ten from four to negative six is subtract ten from negative sixteen negative sixteen subtract ten to that's a cup

of the of the pattern have a common different happening over and over again. Right now let's take a look at the be part a

says find a common difference our ratio is with determined that this is an arithmetic sequence the validity of ratio is

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