SOLUTION: consider the progression 11,8,5,2,....... Determine whether he number -150 is a term of this Progression? Justify by using mathematical rules

Algebra ->  Sequences-and-series -> SOLUTION: consider the progression 11,8,5,2,....... Determine whether he number -150 is a term of this Progression? Justify by using mathematical rules      Log On


   

Question 1139168: consider the progression 11,8,5,2,.......
Determine whether he number -150 is a term of this Progression? Justify by using mathematical rules
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
General term of the arithmetic sequence:
11-3%28n-1%29

Do you find a whole number n, for 11-3%28n-1%29=-150 ?



NO.
n=54%262%2F3

Answer by ikleyn(52788) About Me  (Show Source):
You can put this solution on YOUR website!
.

The first term 11 gives the remainder of 2 when divided by 3, and the common difference of the AP is 3.



It means that every member of the progression gives a remainder of 2 when divided by 3 - but the number -150 

is a multiple of 3, i.e. gives the remainder 0 when divided by 3.



Therefore, the number  -150  is not the term of the progression.

Solved.