Arithmetic Sequence 4th term

  • #1

Main Question or Discussion Point

Our 8th grade math counts team met today and I didnt know how to do this problem:

The first three terms of an arithmetic sequence are p, 2p+6, and 5p-12. What is the 4th term of this sequence?

Please explain how to do this.

Arigato!
 

Answers and Replies

  • #2
please help me
 
  • #3
22
0
Its not an arithmetic progression... and don't bump. In an AP the difference between consecutive terms is constant (i.e. t1-t0=t2-t1 and so forth.) In this case [tex](2p+6)-p=5p-12-(2p+6)[/tex]
[tex]p+6=3p-18[/tex]
[tex]2p=24[/tex]
[tex]p=12[/tex]
Only true when p=12. For all other cases it is not an AP.
 
  • #4
1,065
53
so, is that the solution? p=12 and a difference of 18 between two consecutive numbers?

2p-12 <- simplifies to p, of course, if you know p=12
2p+6
5p-12
5p+6
8p-12
8p+6
.
.
.
 
  • #5
Its not an arithmetic progression... and don't bump. In an AP the difference between consecutive terms is constant (i.e. t1-t0=t2-t1 and so forth.) In this case [tex](2p+6)-p=5p-12-(2p+6)[/tex]
[tex]p+6=3p-18[/tex]
[tex]2p=24[/tex]
[tex]p=12[/tex]
Only true when p=12. For all other cases it is not an AP.
No I believe you are wrong, it IS an arithmetic sequence. Let me explain...

P does equal 12, and the difference between them is 18, so:

an = a1 + (n-1) * d

Plugging in numbers:

an = 12 + (4-1) * 18

so the fourth number is 66

Thanks for your help anyways :)
 

Related Threads on Arithmetic Sequence 4th term

  • Last Post
Replies
4
Views
5K
  • Last Post
Replies
2
Views
2K
Replies
3
Views
1K
Replies
14
Views
7K
  • Last Post
Replies
5
Views
1K
  • Last Post
Replies
3
Views
1K
Replies
2
Views
1K
Replies
14
Views
79K
Replies
9
Views
5K
Replies
4
Views
557
Top