Respuesta :

evyonk

Answer:

397

Step-by-step explanation:

lets say there's an eqn which is y = mx + c, x is the term no. (5, 6 in the egs provided), y is the value corresponding to x (17, 21)

to find the 100th term sequence we need to find m and c. m is how much y changes when x increases by 1

in this case we can find m easily (m = 21-17 = 4)

now we have c left so just sub one of the egs given to what we have alrd found

17 = 4(5) + c

17 = 20 + c

c = - 3

so the eqn is y = 4x - 3, and we can solve for when x = 100

y = 4(100) - 3

y = 397

hope this isn't too confusing :^)

 

boffeemadrid

The 100th term of a sequence is required.

The required term is [tex]a_{100}=397[/tex]

The given terms are

[tex]a_5=17[/tex]

[tex]a_6=21[/tex]

The common difference is

[tex]d=a_6-a_5=21-17\\\Rightarrow d=4[/tex]

The given terms can be expressed as

[tex]17=a+(5-1)4\\\Rightarrow 17=a+16\\\Rightarrow a=17-16\\\Rightarrow a=1[/tex]

The 100th terms is

[tex]a_{n}=a+(n-1)d\\\Rightarrow a_{100}=1+(100-1)\times 4\\\Rightarrow a_{100}=397[/tex]

Learn more:

https://brainly.com/question/22069848?referrer=searchResults

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