LilyMQ
  • LilyMQ
Identify the 35th term of an arithmetic sequence where a1 = -7 and a18 = 95.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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LilyMQ
  • LilyMQ
a. 203 b. 197 c. 168 d. 163
Jhannybean
  • Jhannybean
Define what an arithmetic sequence is first. Do you know general form?
LilyMQ
  • LilyMQ
I have no idea what any of this is lol

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Jhannybean
  • Jhannybean
Alright, so an arithmetic sequence is defined by the general form: \[\large a_n = a_1 + (n-1)d\]
LilyMQ
  • LilyMQ
okay
LilyMQ
  • LilyMQ
how can I calculate the common difference?
Jhannybean
  • Jhannybean
@aric200 no need to criticize.
Jhannybean
  • 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
  • LilyMQ
oooh okay thank you
Jhannybean
  • 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
  • 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
  • aric200
That is all but continue with your explanation.
LilyMQ
  • LilyMQ
@Jhannybean does that mean you are trying to find the 18th term?
LilyMQ
  • LilyMQ
how do I find 'd'?
aric200
  • aric200
She gave you the formula an = a1 + (n – 1)d
LilyMQ
  • LilyMQ
I got a(31)=38+(31-1) but I'm not sure how to find d
Jhannybean
  • 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
  • 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
  • LilyMQ
ooh ok
Jhannybean
  • Jhannybean
So far we have :\[95 =-7+(18 - 1)d\] Are you following?
LilyMQ
  • LilyMQ
yea
Jhannybean
  • Jhannybean
Now can you solve d for me?
LilyMQ
  • LilyMQ
is d 6?
Jhannybean
  • 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
  • Jhannybean
Now that we've found \(d=6\), it should be easy :)
LilyMQ
  • LilyMQ
I got 197 for the answer. Is this correct?
Jhannybean
  • Jhannybean
That is correct :D
LilyMQ
  • LilyMQ
YAY! Thank you so much!
aric200
  • 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
  • LilyMQ
Awesome, thanks guys
Jhannybean
  • Jhannybean
\[a_n= -7 +(35-1)(6)\]\[a_n=-7+204\]\[a_n = 197~ \checkmark \]

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