Question

arithmetic sequences

Answer 1

Find an equation for the nth term of the arithmetic sequence.

-1, 2, 5, 8, ...

Answer 2

can you find the common difference ?

Answer 3

or know what that is ?

Answer 4

its 3 right?

Answer 5

+3

Answer 6

yes!
thats correct :)
d=3

Answer 7

first term = a1 =-1
plug these in
\(\large a_n = a_1 +(n-1)d\)

Answer 8

what ?

Answer 9

sorry, my computer has a tendency to go psyco .-. and the equation would be
an=-1+(n-1)3

Answer 10

correct!
now simplify that :)

Answer 11

-1+3n-3
-4+3n
3n=4
n=4/3

Answer 12

oh, you should not equate it to 0

\(a_n = -1 +(n-1)3 = -1 +3n -3 = 3n -4\)
thats it!

Answer 13

.-. so i did too much? okay.... how does that help the nth term?

Answer 14

\(\huge a_n \implies "the ~n'th ~term"\)

Answer 15

n'th term formula will be dependent on 'n'
here its 3n-4
check it out
plug in n=1
you should get -1

Answer 16

plug in n=2 , you should get 2
and so on

Answer 17

wait..... 3n-4isnt any of these.... whats wrong .-.
an = -1 + 3(n)

an = -1 + 3(n - 1)

an = -1 + 3

an = -1 + 3(n + 1)

Answer 18

wait jk its b!

Answer 19

oh you had choices
then you already have \(-1 +3(n-1)\)
in it, which you found earlier before simplification

Answer 20

Find an equation for the nth term of the arithmetic sequence.

-3, -5, -7, -9, ...

okay so for this one the difference is -2
so the equations -1+(n-1)-2?

Answer 21

ok,
here, the first term is -3
so its
\(\large -3+(n-1)(-2) \)

Answer 22

okay so that first part is always the first number they give you?

Answer 23

sooo -3+ -2n+2
which is... -1-2n

Answer 24

yes, in \(a_n = a_1+(n-1)d\)
that \(a_1\) means the 1st term
the term when n=1

Answer 25

-1-2n is correct :)
but is that in your choices ?

Answer 26

yesss ^.^ okay so workin backwards
Find the first six terms of the sequence.

a1 = 6, an = 2 • an-1

Answer 27

whats an-1?
like the n-1 is below the a

Answer 28

1st term = a1 = 6 is already given

to find 2nd term = a2, we plug in n=2 in an = 2 • a(n-1)

to find 3rd term = a3, we plug in n=3 in an = 2 • a(n-1)
and so on

\(a_{n-1}\) means the 'n-1' the term

Answer 29

like a_n is the n'th term
a_1 is the first term
a_2 is the 2nd term
and so on

Answer 30

.-. math is so confusing.... so 2*a(2-1)

Answer 31

which is 2*a(1) so its 2a

Answer 32

what are your choices ?

Answer 33

6, 12, 14, 16, 18, 20

12, 24, 48, 96, 192, 384

0, 2, 12, 14, 16, 18

6, 12, 24, 48, 96, 192

Answer 34

just lots of numbers

Answer 35

so the 2nd term = 2\(a_1\) = 2 *6 =...
because a_1 = 1st term = 6, we already know!

Answer 36

oh so its d cuz 3*6=24

Answer 37

for 3rd term, put n=3
and yes its 'd'
and no , not because of 3*6

Answer 38

.-. but since n=3 you do 3*6......

Answer 39

\(a_3 = 2 a_{3-1} = 2 a_2\)
but we know that a_2 is 12
\(a_3 = 2a_2 = 2\times 12 =24\)
got this ?

Answer 40

._. nope but i still got to 24 :D

Answer 41

lol
yeah, 24 is correct 3rd term and D is correct answer :)

Answer 42

yay c: thank yous ^.^

Answer 43

welcome ^_^