Question

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

Answer 1

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

Answer 2

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

Answer 3

I have no idea what any of this is lol

Answer 4

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

Answer 5

okay

Answer 6

how can I calculate the common difference?

Answer 7

@aric200 no need to criticize.

Answer 8

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.

Answer 9

oooh okay thank you

Answer 10

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?

Answer 11

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"

Answer 12

That is all but continue with your explanation.

Answer 13

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

Answer 14

how do I find 'd'?

Answer 15

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

Answer 16

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

Answer 17

We are given \(\large a_{18} = a_n = 95\)

That means if we take a closer look at this relation, we see that \(n=18\)

Answer 18

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

Answer 19

ooh ok

Answer 20

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

Answer 21

yea

Answer 22

Now can you solve d for me?

Answer 23

is d 6?

Answer 24

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 \(n=35\)

Answer 25

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

Answer 26

I got 197 for the answer. Is this correct?

Answer 27

That is correct :D

Answer 28

YAY! Thank you so much!

Answer 29

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

Answer 30

Awesome, thanks guys

Answer 31

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