arithmetic sequence

[r0b]

Hi, can somebody help me please with this arithmetic sequence?

specify the first 5 parts of arithmetic sequence.
3.part + 12.part + 8 = 0
8.part + 1.part - 4.part = 1


Thank you.

 

[Harry_the_cat]

I don't understand your notation??

 

[Deleted member 4993]

Hi, can somebody help me please with this arithmetic sequence?

specify the first 5 parts of arithmetic sequence.
3.part + 12.part + 8 = 0
8.part + 1.part - 4.part = 1


Thank you.

What does "part" mean in this context?

 

[r0b]

What does "part" mean in this context?

a term, a1 for example is the first term, 3. part is a 3rd term. I didnt know the right word, sorry for that.

 

[HallsofIvy]

I assume your "3.part" is the third term in the sequence, "12.part" is the twelfth term, etc.

An "arithmetic sequence" has a "common difference" and is of the form "a, a+d, a+2d, a+3d, ....". The third term is a+ 2d and, generally, the nth term is a+ (n-1)d.

So "3.part + 12.part + 8 = 0" means that a+ 2d+ a+ 11d+ 8= 2a+ 13d+ 8= 0 and
"8.part + 1.part - 4.part = 1" means that a+ 7d+ a- (a+ 3d)= a+ 4d= 1.

Solve the two equations, 2a+ 13d= -8 and a+ 4d= 1 for a and d.

 

[r0b]

I assume your "3.part" is the third term in the sequence, "12.part" is the twelfth term, etc.

An "arithmetic sequence" has a "common difference" and is of the form "a, a+d, a+2d, a+3d, ....". The third term is a+ 2d and, generally, the nth term is a+ (n-1)d.

So "3.part + 12.part + 8 = 0" means that a+ 2d+ a+ 11d+ 8= 2a+ 13d+ 8= 0 and
"8.part + 1.part - 4.part = 1" means that a+ 7d+ a- (a+ 3d)= a+ 4d= 1.

Solve the two equations, 2a+ 13d= -8 and a+ 4d= 1 for a and d.

so a1=9; a2=7; a3=5; a4=3; a5=1 and the sum is 25?

 

[Deleted member 4993]

so a1=9; a2=7; a3=5; a4=3; a5=1 and the sum is 25?

Why are you calculating the "sum" of the terms?

You have "?" after you calculated the sum. Why don't you have confidence in your work?

 

[r0b]

Why are you calculating the "sum" of the terms?

You have "?" after you calculated the sum. Why don't you have confidence in your work?

the teacher wants us to calculate the sum of the terms.
And I have "?" there because I wanted to know if I solved the equations correctly. The sum from the task is correct, so the terms are too.

Thank you.

 

[Steven G]

Why not tell us the entire question in your 1st post?

 

[Harry_the_cat]

Why not tell us the entire question in your 1st post?

Because once we helped get the first 5 terms, he/she would have had no trouble finding the sum.