Question

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

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

an = -1 + 3(n)

an = -1 + 3(n - 1)

an = -1 + 3

an = -1 + 3(n + 1)

Answer 1

@sauravshakya @phi @Hero

Answer 2

plug in n=1 and see which eqn gives you ans -1 as -1 is your first term ;)

that was the layman method..

Answer 3

otherwise,,you need to read a book on AP i guess..the first page or second page of that shall provide you the ans..

Answer 4

that doesnt help me...

Answer 5

i see..

Answer 6

:P

Answer 7

can you show me how to solve this?

Answer 8

what the nth term of an AP ?
you must be knowing what an AP is right ?

Answer 9

Before even looking at the choices, I would look at the progression and find the difference between each number.

Answer 10

3

Answer 11

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

I would notice that 2 - -1= 3
5-2=3
8-5=3

so I expect the numbers to go up by 3 (seems obvious?)

Answer 12

yes

Answer 13

now I would look at the choices.

the first one says
an = -1 + 3(n)

that 3 in 3n looks good. But I notice all the choices have a 3 in them...
How do we pick the right choice?

use shub's idea
if n=1 (that means the first term, term number 1)
we replace the n with 1
a1 (that just means the value of the first term) is -1 + 3*1= -1+3=2
2 does not match -1 (which is the first term in -1, 2, 5, 8, ...

Answer 14

can you check the 2nd choice
an = -1 + 3(n - 1)

Answer 15

-1+3*1=-1+3=2???

Answer 16

that is the first choice an= -1+3n

check
an = -1 + 3(n - 1)

everywhere you see n, put in 1.
then do the arithmetic (but remember an becomes a1, and that is just a name)

Answer 17

a1=-1+3(1-1)

Answer 18

yes, exactly. now what is (1-1)?

Answer 19

0

Answer 20

yes, so what is
a1=-1+3(1-1)

Answer 21

2

Answer 22

?

Answer 23

oh wait, 0

Answer 24

that way you simplify
a1=-1+3(1-1)

is to do the subtraction in the parens (1-1). replace the (1-) with the answer 0
a1= -1 +3*0
now do 3*0
add to -1

Answer 25

* replace the (1-1) with the answer 0

Answer 26

3*0+ -1?

Answer 27

three times zero plus -1

Answer 28

-1

Answer 29

so the 2nd choice tells you
a1= -1
this formula gives -1 as the 1st term. That matches the first term of
-1, 2, 5, 8, ...

so this might be the answer. Check the formula with n=2 to see if you get a 2

Answer 30

can yo do that?

Answer 31

a2 = -1 + 3(2 - 1)?

Answer 32

yes, keep going.

Answer 33

2!

Answer 34

Yes,
a2= -1 +3*(2-1)
2-1 is 1 so
a2= -1+3*1
a2= -1+3
a2=2

so choice 2 looks like it's the answer.

you could check that choices 3 and 4 do not work, but that is not necessary, except if you want to practice.

Answer 35

thank you! :)