Determine the second and third terms of an arithmetic sequence if
A)the first term is 6 and the 4th term is 33
Thanks)

Question

Determine the second and third terms of an arithmetic sequence if 
A)the first term is 6 and the 4th term is 33
Thanks)

strawberry17 · Answer

It is going up by 9 :)

directrix · Answer

The two terms given are the fourth terms and the first terms.

The fourth term = the first term + 3*d which is the common difference

33 = 6 + 3d

d = 9 as @strawberry17 determined by inspection which is releatively easy when the common difference is an integer.

directrix · Answer

If the first term is 6, then then the second term will be 6 + 9 and the third term will be 6 + 2*9.

The fourth term should be 6 + 9*3. If that cranks out to be 33, then the above work is correct. 

So, @noname81 what are the the second and third terms of the sequence? Post, and we will check them, okay?

anonymous · Answer

Im am trying to get use to the Tn=t1+(n-3)d formula I could have used logic to solve the equation but I would like to use this formula.

anonymous · Answer

I think that the 33=6+d will help. I can punch in the numbers into the equation. D=9 T1=6 n=3. 
Does that look about right ?

directrix · Answer

Okay, let's use that formula.

Hold on.

directrix · Answer

The fourth term = 33

The first term = 6

Since t4 and t1 are (four - one = 3) places apart, then I know from the definition of an arithmetic sequence that t4 = t1 + 3*d. Using this, I can then solve for the common difference d.

33 = 6 + 3*d
Solve for d.
The common difference is 9.  Do you agree @noname81   Questions?

anonymous · Answer

got it

directrix · Answer

The n-th term of an arithmetic sequence is of the form tn = t1 + (n – 1)d.

Find t2 in the posted problem.

t2 = t1 + (2-1)*9 = 6 + 1*9 = 15 for the second term.

anonymous · Answer

awsome  crystal clear now. Thank you :)

directrix · Answer

Third Term:

t3 = t1 + (3-1)*9 = 6 + 2*9 = 6 + 18 = 24  --> See if you agree @noname81 

I apologize for my "false starts."  But, I wanted to get the terminology right so that you can work all of these types of problems.

directrix · Answer

Here's a link to a great study resource: http://www.purplemath.com/modules/series.htm On the last two pages of that section are worked out solutions. Helpful.

anonymous · Answer

thanks

directrix · Answer

Glad to help.