Arithmetic sequences

[HNO]

Hi there,

1. Determine the position of the given terms to complete the following statement:

a. -14 is the _ term of 2 1/5, 2, 1 4/5...

So I found d (Common Difference) which is 1/5. And I put the # into term 1,2,3 and used the formula Tn = t1 + (n-1)d

I keep getting weird answers and my teacher tolled us the answer was 82. But I want to know how he did that so incase it is on the test I will know as he would not go over it in class.

PLEASE HElP … who ever helps in great and I can not tell you how much it means to me (=

 

[tkhunny]

Again, first term is 2 1/5
Common difference is -1/5 <== You said it is positive. Not so!

First, "2 1/5" is SUPER clunky. Let's switch to something reasonable. 2 1/5 = 11/5. Do you know how to do that?

1) 11/5
2) 11/5 - 1/5
3) 11/5 - 2(1/5)
4) 11/5 - 3(1/5)
5) 11/5 - 4(1/5)
...
n) 11/5 - (n-1)(1/5)

Solve: 11/5 - (n-1)(1/5) = -14

 

[HNO]

Arithmetic

Again, first term is 2 1/5
Common difference is -1/5 <== You said it is positive. Not so!

First, "2 1/5" is SUPER clunky. Let's switch to something reasonable. 2 1/5 = 11/5. Do you know how to do that?

1) 11/5
2) 11/5 - 1/5
3) 11/5 - 2(1/5)
4) 11/5 - 3(1/5)
5) 11/5 - 4(1/5)
...
n) 11/5 - (n-1)(1/5)

Solve: 11/5 - (n-1)(1/5) = -14

Solve: 11/5 + ( n-1)(1/5) = -14 ( is it not suppose to me a adding sign…. that is in my formula?) If I did make it a plus here is what i do….:

-14= 11/5 + (n-1)(1/5)

-14= 11/5 + 1/5n -1/5

-14/1 - + 1/5 then subtract 11/5 ( But to do this keeping it in fraction form don't I need to find a common denominator? as my teacher says keep it in fraction form no decimals! so 5 is common so does -14/1 become -70/5? -80/5 >>>-16 = 1/5 n now how do i divide this …

Thank you so much for helping me

 

[tkhunny]

( is it not suppose to me a adding sign…. that is in my formula?) If I did make it a plus here is what i do….:

I don't know what this means.

11/5 - (n-1)(1/5) = -14

Why not simplify your life? Multiply by 5

11 - (n-1) = -70

SO much simpler!

 

[HNO]

Arithmetic

This helped so much last question is >>>> I use the formula Tn = T1 + (n-1)d

Why does the plus sign after t1 become a a subtraction sign after wards -14 = 11 - (n-1)

Subtracting gives me the correct answer but I want to know how exactly it got there ….. was it just how it worked out in simplifying?

Apologize for all the questions on this one ** but you have helped me so much (=

 

[HNO]

This helped so much last question is >>>> I use the formula Tn = T1 + (n-1)d

Why does the plus sign after t1 become a a subtraction sign after wards -14 = 11 - (n-1)

Subtracting gives me the correct answer but I want to know how exactly it got there ….. was it just how it worked out in simplifying?

Apologize for all the questions on this one ** but you have helped me so much (=

***** Oh is it because 1/5 =d was negative so it was -1/5n > -1n so you just put it b4 I GET IT!

 

[HNO]

For your benefit: please do not use "bad English" like b4 for before.
-(a - b) = -a + b : understand?

Hope u r ok!

thank you I get it … I do not use that formula but I get how u got that. Sorry about the b4 and before ….. my iphone sometimes autocorrects and I was out so I had to use my iphone. Sorry will not happen again

 

[HallsofIvy]

***** Oh is it because 1/5 =d was negative so it was -1/5n > -1n so you just put it b4 I GET IT!

Actually it is NOT because "1/5= d" was negative (1/5 is NOT negative), it is because d= -1/5, NOT 1/5. Your initial sequence was "2 1/5, 2, 1 4/5...": 2 1/5- 1/5= 2, 2- 1/5= 1 4/5, so then 1 4/5- 1/5= 1 3/5, 1 3/5- 1/5= 1 2/5,.... You could answer this by continuing to subtract 1/5 (really "add -1/5") until you get down to -14. But actually doing that is much more tedious that just asking "how many "steps" of 1/5 are there from 2 1/5 to -14"? From 2 1/5 to -14 is a "distance" of 2 1/5-(-14)= 11/5+ 70/5= 81/5. And it should be obvious from that fraction how many "steps" of 1/5 there are. More formally, you would divide that fraction by 1/5- remembering to "invert and multiply".