Identify the 35th term of an arithmetic sequence where a1 = -7 and a18 = 95.

- LilyMQ

Identify the 35th term of an arithmetic sequence where a1 = -7 and a18 = 95.

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- LilyMQ

a. 203
b. 197
c. 168
d. 163

- Jhannybean

Define what an arithmetic sequence is first. Do you know general form?

- LilyMQ

I have no idea what any of this is lol

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- Jhannybean

Alright, so an arithmetic sequence is defined by the general form: \[\large a_n = a_1 + (n-1)d\]

- LilyMQ

okay

- LilyMQ

how can I calculate the common difference?

- Jhannybean

@aric200 no need to criticize.

- Jhannybean

n = the number of terms you're looking for in the sequence
d = difference between the terms (preceding number - previous number)
\(a_1\) = the first value in the sequence of numbers.

- LilyMQ

oooh okay thank you

- Jhannybean

So if we have \(a_{\color{red}n} = a_{\color{red}{18}}\) what does that tell you about the number of terms in the sequence?

- aric200

I'm simply trying to say your teacher more than likely gave you background on what you are doing in less this is a pretest in which you should not even be asking for our help, but If not then I'm sure there is text that pertains to this type of math and going back over that could help you get a better understanding. Thats the best thing to do when you "have any idea what this is"

- aric200

That is all but continue with your explanation.

- LilyMQ

@Jhannybean does that mean you are trying to find the 18th term?

- LilyMQ

how do I find 'd'?

- aric200

She gave you the formula
an = a1 + (n – 1)d

- LilyMQ

I got a(31)=38+(31-1) but I'm not sure how to find d

- Jhannybean

We are given \(\large a_{18} = a_n = 95\)
That means if we take a closer look at this relation, we see that \(n=18\)

- Jhannybean

This is basically telling us that if we had a 18 numbers in a sequence, our value of \(a_n\) would be 95.

- LilyMQ

ooh ok

- Jhannybean

So far we have :\[95 =-7+(18 - 1)d\] Are you following?

- LilyMQ

yea

- Jhannybean

Now can you solve d for me?

- LilyMQ

is d 6?

- Jhannybean

Yes, so \(d=6\).
Now we're trying to find the 35th term in the sequence, this means we are trying to find \(a_n\) when \(n=35\)

- Jhannybean

Now that we've found \(d=6\), it should be easy :)

- LilyMQ

I got 197 for the answer. Is this correct?

- Jhannybean

That is correct :D

- LilyMQ

YAY! Thank you so much!

- aric200

Here it is all together for you and anyone else who stumbles upon this question later. Makes it less complicated in my opinion but good job.
x(n)=a+d(n-1)
95=-7+d(18-1)
95=-7+d(17)
95+7=d(17)
102=17d
d=102/17
d=6
After finding D plug it in
x(35)=-7+6(35-1)
x(35)=-7+6(34)
x(35)=-7+204
x(35)=197
So the answer is B) 197

- LilyMQ

Awesome, thanks guys

- Jhannybean

\[a_n= -7 +(35-1)(6)\]\[a_n=-7+204\]\[a_n = 197~ \checkmark \]

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