What is the nth term in the sequence 3, 7, 11 . . .?
4n + 2
4n − 1
4n + 3
3n + 2
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TheSmartOne (thesmartone):
Plug in n=3
Into each answer choice. And whichever one gets you 7 will be your answer
OpenStudy (anonymous):
b
OpenStudy (anonymous):
gets you 7?
TheSmartOne (thesmartone):
For example
4(3)+2 = 14
That is not 7, so A is wrong.
OpenStudy (anonymous):
none of gets me 7
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OpenStudy (anonymous):
???
TheSmartOne (thesmartone):
Are you sure you posted the correct answer choices?
OpenStudy (anonymous):
Im 100%
TheSmartOne (thesmartone):
Well then there is something wrong with the answer choices, or with the question.
OpenStudy (anonymous):
freckle help me out wouldnt it be A
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OpenStudy (anonymous):
cause its a pattern
OpenStudy (anonymous):
they go up 1 each number
OpenStudy (freckles):
\[a_n=a_1+d(n-1)\]
this is going to be the nth term
OpenStudy (freckles):
a_1 is the first number
OpenStudy (freckles):
d is the common difference
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OpenStudy (freckles):
can you identify both of those for me please?
OpenStudy (anonymous):
I mean they go down 1
OpenStudy (anonymous):
so it would be 5,4,3
OpenStudy (freckles):
7-3 isn't 1
OpenStudy (anonymous):
5,4,3,2
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OpenStudy (freckles):
can you tell me please what the first number is in your sequence
that will be a_!
OpenStudy (freckles):
a_1
OpenStudy (anonymous):
3,7,11,13
OpenStudy (freckles):
I want you to identify for me
what a_1 is (which is also known as the first number in your sequnce)
and also d (which is known as the common difference)
OpenStudy (anonymous):
4(3)+3=16
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OpenStudy (freckles):
d can be found by doing either of these differences:
7-3
11-3
or
13-3
OpenStudy (anonymous):
ok
OpenStudy (anonymous):
It has to be C
OpenStudy (freckles):
can you tell me what both of the numbers I asked for are?
and we will have the answer shortly after that
OpenStudy (anonymous):
ok
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OpenStudy (anonymous):
a1=3
OpenStudy (freckles):
and d?
OpenStudy (anonymous):
-3
OpenStudy (freckles):
no d is the common difference
it can found by doing
7-3
or
11-7
(oops I didn't meant to put 13-3 or whatever earlier; lol)
the point is 7-3 and 11-7 are both 4
there is a common difference
we do have an arithmetic sequence
a1=3 and d=4
plug them in
\[a_n=a_1+d(n-1) \\ a_n=3+4(n-1)\]
distribute and combine like terms and you are done!
OpenStudy (anonymous):
3n-3 4n-4
7n-7
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OpenStudy (freckles):
no :(
OpenStudy (freckles):
3+4(n-1)
3+4n-4
can you combine like terms now?
OpenStudy (freckles):
what is 3-4?
OpenStudy (anonymous):
1
OpenStudy (freckles):
-1 right?
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OpenStudy (anonymous):
-1
OpenStudy (freckles):
3+4(n-1)
distribute
3+4n-4
4n+3-4
4n-1
OpenStudy (anonymous):
my fault was quick to answer that 3-4
OpenStudy (freckles):
as you see this gives you your sequence
for n=1 we have 4(1)-1=4-1=3
for n=2 we have 4(2)-1=8-1=7
for n=3 we hve 4(3)-1=12-1=11
and so on...
OpenStudy (anonymous):
the other guy told me to plug in 3
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OpenStudy (freckles):
I can't explain that
But I can explain why 4n-1 is the answer :p
OpenStudy (freckles):
as I did above
do you still not understand somethin?
OpenStudy (anonymous):
Yea I understand now sorry for acting like a dumb retrice
OpenStudy (freckles):
No! You aren't dumb.
OpenStudy (freckles):
It is called learning. And we can all feel dumb when learning but you aren't actually dumb.
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