week 17 – math 10

This week we continued to further our knowledge of arithmetic sequences, and something I learned was how to find the difference in a sequence if you are not given 2 terms beside each other. in  pattern.

for example we will use: t1 = 2,  t4 = 10 d = ?

first you have to find how many differences you are changing by, by subtracting the term numbers (n) from each other:

4-2 = 2 differences between the terms

no we put the information into our formula:

t1 + 2d = t4

2  + 2d = 10

Now we let  algebra take over to the difference of the pattern:

2d = 10-2

2d = 8

2d/2 = 8/2

d = 4

Now we know our difference, and if you wanted to find tn (the formula of the pattern) then you just put in the info:

tn = t1 + (n-1) d

tn = 2 + (n-1) 4

now we simplify

tn = 2 + 4n – 4

tn = 4n – 4 + 2

tn = 4n – 2

now we can find all of the terms in the pattern

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