Question

What are the first five terms of the sequence given by the formula?

Answer 1

\[a _{n} = 5n + 1\]

Answer 2

@jdoe0001 can you please help me? i am SO stressed out and I'm SO behind on my work

Answer 3

Well Lets start off with n=1

Answer 4

\[a_1=5(1)+1=5+1=6\]
So \[a_1=6\]

Answer 5

Now continue plugging in n=2 and n=3 n=4 and n=5

Answer 6

this might help these are the choices i have!

Answer 7

how did you get the 1? I'm sorry i just don't understand any of this…why did you choose those numbers to plug in? @BlackLabel

Answer 8

Well the first term is \[a_1\]

Answer 9

i just don't understand any of this I'm sorry I'm completely lost

Answer 10

Lets start explaining sequences from the beggining

Answer 11

alright thanks

Answer 12

Okkkk a sequence is a bunch of terms with a pattern

Answer 13

alright

Answer 14

Okkk so we have Term #1, Term #2, Term#3 , Term #4 ..... It goes on forever

Answer 15

alright!

Answer 16

omg i think i get it! would it be the second choice?

Answer 17

Now Let each term be known as
\[a_n\]
where n stands for the number of term
So for example \(a_1\) is the first term of the sequence and \(a_2\) is the second term of the sequence

Answer 18

oh nvm those answer choices are wrong.

Answer 19

\(\Large a_{\color{red}{ n}}=5{\color{red}{ n}}+1\qquad
\begin{array}{llll}
term&value\\
\hline\\
1 & a_{\color{red}{ 1}}=5({\color{red}{ 1}})+1\\
2& a_{\color{red}{ 2}}=5({\color{red}{ 2}})+1\\
3&a_{\color{red}{ 3}}=5({\color{red}{ 3}})+1\\
4&a_{\color{red}{ 4}}=5({\color{red}{ 4}})+1\\
5&a_{\color{red}{ 5}}=5({\color{red}{ 5}})+1
\end{array}\)

Answer 20

i finally understand what you were doing, when you were plugging in the values, would it be: 6,11,16,21,26?

Answer 21

Yup

Answer 22

does it matter what numbers you pick to plug into the equation? @jdoe0001

Answer 23

Thanks so much! @BlackLabel

Answer 24

nope, that's the idea, the equation is very general

Answer 25

Well it does matter in this case. It asked for the first 5 terms so we have to plug n=1,2,3,4 and 5

Answer 26

oh wow! thanks! could you help me with another one? idk how to solve it!

Answer 27

and voila you get your answer

Answer 28

thanks so much!!! @BlackLabel

Answer 29

i have no clue how to do this! @BlackLabel

Answer 30

Ok Lets start off with what our first term of the sequence is
\( a_1\) is the first term of the sequence
So what is \( a_1\)?

Answer 31

11?..

Answer 32

Yes

Answer 33

alright, now what?

Answer 34

\(\bf a_1\implies \textit{1st term in the sequence, or the }\)

Answer 35

Next we subtract the first term from the second term to see if this is an arithmetic sequence sooo ----> 8-11=-3
Now we check the next 2 terms ----> 5-8 = -3
Then we check the third term ----> 2-5 = -3
If you notice the difference btwn all 4 terms are the same

Answer 36

Soo we can then assume that the sequence has a pattern such that each term is 3 less than the term before

Answer 37

In other words a term is the previous term -3

Answer 38

so its the second choice? (:

Answer 39

Yup

Answer 40

omg thankyouuuu(: i have to go, will you be on later???