equations with nth term?

Question

a) write down as simply as possible an expression for the nth term of the sequence.....
100, 96, 92, 88,.....

b) One of the terms of this sequence is -260. which term is it?

c) Is -150 a term of this sequence? Explain your answer.


thanks!

Answer 1

YOU IN X?
a)
a= 100, d= -4
a(n) = a+(n-1)d=100+4-4n =104-4n

b) 104-4n= -260
.: n= 91
c)

Answer 2

This is an AP with common difference -4. nth term is
100+ (n-1)*(-4)=-4n+104.
1.-260=-4n+104, hence n=91 or 91st term
2.If -150 is nth term, then -150=-4n+104 or n= -254/4 whcih makes n a fraction. n cannot be a fraction. Hence -150 cannot be a term in the series.

Answer 3

a) 104-4n (assuming u start at n=1)

b) if 104-4n = -260 then 4n= 364 so n = 91

c) if -150 = 104-4n then 4n = 254 so n=63.5
this is not possible, since n must be a whole number. so -150 is not a term