Question

The first negative term in the arithmetic sequence 2006, 1998, 1990, ... is ?

Answer 1

continus the pattern for a few terms, what do you notice?

Answer 2

d=-8

Answer 3

2006-1998=-8

Answer 4

oh right you mean d is the common difference, thats correct,

Answer 5

yes

Answer 6

do you know the formula for the nth term of an Arithmetic sequence?

Answer 7

\[T(n) = a+(n-1)d\] where a is the first term, n is the number of terms and d is the common difference. We want the term than is negative.
So find \[T(n) = a + (n -1)d < 0\] and solve for n. This will tell you which term of the arithmetic sequence is first negative. Then to find the actual value of the term again resort to the formula for the nth term in the sequence.

Answer 8

2006+(n-1)(-8)<0

Answer 9

o solve
2006+(n-1)(-8)<0

you could distribute the -8 (which means multiply -8 times each term inside the parens) and get
2006 -8n + 8 < 0

add +8n to both sides. also, simplify 2006+8
2014 -8n + 8n < 8n
2014 < 8n
divide both sides by 8
2014/8 < n

Answer 10

so you get n<251.75 ?

Answer 11

you mean n> 251.75

so the first negative term is for n=252
use your formula to figure out its value

Answer 12

however the choices given are:
A.-8
B. -6
C. -4
D. -2

Answer 13

what do you get for T(n), using
T(n) = a+(n-1)d

when n= 252

Answer 14

-2 then

Answer 15

okay, i miss it

Answer 16

yes, so choice D.

Answer 17

thx