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

a.) The sequence decreases by 4 with each term. To write the expression, add 4 to the first term (to define the zeroth term), and then subtract 4n:
x = 104 - 4n.

b.) Set the expression equal to -260:
-260 = 104 - 4n
-364 = -4n
91 = n

c.) 2 methods:
1.) Since the terms decrease by 4, and are all divisible by 4, you can tell -150 isn't a term, because -150 isn't divisible by 4.
2.) -150 = 104 - 4n solves with n = 65.5. If n is not an integer, then -150 isn't a term.

Answer 2

a)suppose U1=100, d=4.........(from; 100-96=4)
Un=d+Un-1
Un=4+Un-1

b) U-260=?
U1=100, U2=96, d=4
U-260=U1+(n-1)d
=100+(-260-1)4
=100+(-261)4
=100-1044
U-260 = -944


c)!!!!!!!!!! i didn't get it!!!!!!