SOLUTION: The problem is to find the general equation for the sequence, {-1,3,-5,7,-9,11,-13,15...}. I know that -1+4=3;-1-4=-5; -1+8=7;-1-8=-9; etc...so I am guessing it involves 4*n since

Question 31731: The problem is to find the general equation for the sequence, {-1,3,-5,7,-9,11,-13,15...}. I know that -1+4=3;-1-4=-5; -1+8=7;-1-8=-9; etc...so I am guessing it involves 4*n since the difference between the numbers is 4,8,12,16,20,24,28 respectively. Also, the alternating signs indicate -1^n. I also wondered if it involved absolute value. I just haven't been able to put it together with the formula for an arithmetic sequence.
Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
The problem is to find the general equation for the sequence, {-1,3,-5,7,-9,11,-13,15...}. I know that -1+4=3;-1-4=-5; -1+8=7;-1-8=-9; etc...so I am guessing it involves 4*n since the difference between the numbers is 4,8,12,16,20,24,28 respectively. Also, the alternating signs indicate -1^n. I also wondered if it involved absolute value. I just haven't been able to put it together with the formula for an arithmetic sequence.
YOU ARE ON RIGHT TRACK...THIS IS AN ALTERNATING SEQUENCE WITH 2 FORMULAE FOR N TH.
TERMS
ODD TERMS ARE .....-1,-5,-9,-13....ETC
SO A=-1,CD=-5+1=-4.....SO TM FOR THIS IS TM=-1-4(M-1)=-1-4M+4=3-4M....WE USED M HERE INSTEAD OF CONVENTIONAL N WHICH IS RESEVED FOR THE ORIGINAL SERIES
SO WHEN N IS ODD OR FOR T(2N-1)..THIS IS THE FORMULA
T(2N-1)=3-4N
NOW EVEN TERMS ARE...3,7,11,15.......ETC....BUT THESE ARE STARTING FROM SECOND TERM IN THE SERIES
SO A=3,CD=4...........TR=3+4(R-1)=4R-1
SO WHEN N IS EVEN WE HAVE ...FOR T2N...THIS IS THE FORMULA
T2N=4N-1..................
THUS THE SERIES IS DEFINED BY 2 FORMULAE(LIKE WE DO FOR FUNCTIONS IN DIFFERENT RANGES)
T(2N-1)=3-4N AND T2N=4N-1.
RELATED QUESTIONS
Find the nth term of the sequence 1/5, 1/3, 3/7, 1/2, 5/9, 3/5, 7/11, 2/3, 9/13,... (answered by lynnlo)

find the equation of the line passing through the points a. (1,3) et (3,6) b. (-2, -5)... (answered by solver91311)

2/3+3/4=? 1/4+5/6=? 3/4+1/5=? 2/3+5/9=? 1/9+5/6=? 2/3+4/5=? 1/3+7/8=?... (answered by edjones)

Write the general term for the following sequences: 1. 1/2, 1/3, 1/4, 1/5, ... 2. 1,... (answered by josgarithmetic)

What is the next three terms of the sequence, 1/5, 2/7, 4/9, 8/11,... (answered by Alan3354)

What is the next three terms of sequence, 1/5, 2/7, 4/9, 8/11,... (answered by Theo)

Give the next three terms for each sequence 1/5, 2/7, 4/9, 8/11, 16/3 (answered by ikleyn)

Calculate the area of the triangle with the following vertices: 6. (-3, -3), (0, -3), (answered by Alan3354)

what's the formula for this sequence 1, -2, 3, -4, 5, -6, 7, -8, 9,... (answered by Edwin McCravy)