Help me solve this please~~

[Yuuka]

Show that the arithmetic mean for the term 2x+7 and 43-6x is 25-2x. Then, calculate x if given 8th term is 13

Thanks guys~ (the first part can be ignored)

 

[HallsofIvy]

You only give two numbers so what do you mean by "the eighth term"? The eighth term of what

 

[Yuuka]

You only give two numbers so what do you mean by "the eighth term"? The eighth term of what

I have no idea. This is the question that I get. I assume that it means the 8th term of the progression include the 2 numbers with unknown given. But the question doesn't even the position of the two terms thats why Im having problem with this question...

 

[Ishuda]

From the first part, the 2x+7, 43-6x, and 25-2x are term values and not term numbers. Normally one would expect that they would be for the same term number but the second part seems to contradict that.

For the second part, 'calculate x if given 8th term is 13', x can not be the number of the term if the second part is to make sense. So whether it is the 8th term or the 3925th term makes no difference. There is a term and the value is 13. But that still leaves the question 'term of what (sequence)?'.

Do all three
2x+7 = 13 => x=3
43-6x= 13 => x=15
25-2x= 13 => x=6

So, either the relationship between x and the term number is different for each of the sequences, or the average is for two different term numbers with the result being yet a different term number.

Or maybe, just maybe, the sun rose in the west today and everyone wins.

 

[Yuuka]

This has got to be one of the most silly/confusing problem I've seen

Answer is x=6; 2 series exist:
27,25,23,21,19,17,15,13 : x = -1,0,1,2,3,4,5,6
-1,1,3,5,7,9,11,13 : x = 13,12,11,10,9,8,7,6

Each term = 25-2x

I have to agree with you, this question is seriously so confusing and it's giving me a hard time.

Anyway, thank you guys for your help in this questions~! I guess I will go with Denis's answer

 

[HallsofIvy]

OH! The shame!