How to Work out the nth term in the sequences below?
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Note: I keep asking this and I get a formula:
nth term = dn + (a - d)

- anonymous

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- katieb

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- anonymous

@lgbasallote
@nincompoop

- anonymous

Please help:(

- lgbasallote

what exactly are you asking?

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## More answers

- lgbasallote

sequence of what?

- anonymous

I dont undersyand how to create a formula.

- anonymous

The worksheet is at the link above.

- lgbasallote

i see many sequences

- anonymous

It says you have to work out the terms asked for, create a formula.

- anonymous

Actually,all of them. I uave to turn this in today.

- lgbasallote

well...the formula for arithmetic sequence is what you say \[\huge a_n = a_1 + (n-1)d\]
where:
an is the last term
a1 is the first term
n is the number of terms
d is the common difference

- anonymous

Please know I am in eight grade.

- lgbasallote

for example
1, 9, 17, 25, 33,...
find the 50th term
an would be a50 because a50 is the last term
a1 will be 1 because it's the first term
n would be 50 because you're looking for the 50th term so you have 50 terms
d would be 8 because it adds 8 each number (1 + 8 = 9; 9 + 8 = 17; etc)
so if you substitute.. \[\huge a_{50} = 1 + (50 - 1)8\]
\[\huge a_{50} = 1 + 49 (8)\]
\[\huge a_{50 } = 1 + 392\]
\[\huge a_{50} = 393\]
so the 50th term is 393 in my example

- lgbasallote

if you're old enough to learn sequences then you're old enough to learn this

- anonymous

Ok..'reading'

- anonymous

may i try o e?

- lgbasallote

sure

- anonymous

From my homework.

- anonymous

ill write in othere first amd then type it on here.

- lgbasallote

sure

- anonymous

a44=8+(5-1)9

- anonymous

number 7

- anonymous

is that correct?

- lgbasallote

let me check...

- anonymous

ok

- lgbasallote

number 7 is looking for the 50th term not the 44th

- anonymous

You said a1 was the last term,which in this case is 44

- lgbasallote

i think you're confused...
8, 17, 26, 35, 44, ....
this doesn't mean 44 is the last term
"..." means the sequence continues
8, 17, 26, 35, 44, 53, 62, 71 and so on

- lgbasallote

that means the last term is the 50th term because that's what you're looking for
make sense?

- anonymous

ohhhh

- anonymous

well, if we erased the 44, would it be correct?

- lgbasallote

nope. you used 5 as your n

- anonymous

im sorry.

- lgbasallote

like i said, the sequence doesn't stop at 44 so there are more than 5 terms

- lgbasallote

since you're looking for the 50th term, there would be 50 terms
make sense?

- anonymous

yes

- lgbasallote

good. so rewrite your solution

- anonymous

wait it shouldve been 50 right

- anonymous

a50=8+(50-1)9

- lgbasallote

right. now solve it

- anonymous

thatll give me the 50th term?

- anonymous

do you solve for a in the a50?

- lgbasallote

no... a50 means \(a _{50}\) that means 50th term

- lgbasallote

just solve the right side

- anonymous

-2?

- anonymous

n

- anonymous

no

- lgbasallote

how'd you get -2?

- anonymous

umm,let me tru again

- anonymous

web2.0calc

- anonymous

ooo the a50 doesnt matter when solving

- lgbasallote

yes

- anonymous

513?

- anonymous

i lost connection

- anonymous

back,

- anonymous

was i right?

- lgbasallote

you solved 8 + (50-1)9
right?

- anonymous

yes

- lgbasallote

did you use a calculator?

- anonymous

yes
i was supposed to use order of operations?

- lgbasallote

i see what you did
(8 + 50 - 1)* 9

- lgbasallote

that is wrong

- anonymous

*sigh* ok

- lgbasallote

you have to do (50 -1)
then multiply it to 9
then add 8

- anonymous

order of ops.

- lgbasallote

PEMDAS
PARENTHESIS
expoent
MULTIPLICATION
division
ADDITION
subtraction
did you forget this?

- anonymous

no,
thats what order of operations is

- lgbasallote

parenthesis is (50 - 1)
multiplication is (50-1)*9
addition is 8 + (50-1)*9

- lgbasallote

that means you do 50 - 1 first

- anonymous

o. so, i use that formula, substitute,and solve right side?

- lgbasallote

yes

- anonymous

THANK YOU

- lgbasallote

welcome

- anonymous

hi amistre

- lgbasallote

i hope im not in trouble @amistre64

- amistre64

finally got to the end of it :) howdy!

- anonymous

howdy,sir

- anonymous

you mean the end of my endless question?

- amistre64

i havent seen the links yet, but lgbas stuff looks good so far
yeah, these things can get rather lengthy, but thats the way we like to see them. lots of interaction and studying instead of rote answers

- anonymous

am i in trouble

- amistre64

lol, not that i can see :) as long as your trying to learn that material you are fine

- anonymous

yes imam.

- amistre64

they all look to be arithmetic progressions, so you can apply the same techniques to all of them

- lgbasallote

i'd like to know though @amistre64 do you know what dn + (a-d) means?

- lgbasallote

it looks like the formula for arithmetic progression....but it looks weird

- amistre64

its another way to express the sequence but for n starting at 0 i believe

- anonymous

amistre can i fan u

- lgbasallote

dn looks really weird

- amistre64

dn + (a-d)
dn - d + a
d(n-1) + a

- amistre64

you can fan whomever you wish

- lgbasallote

...clever

- amistre64

i think if i get anymore fans the site will collapse into an infinitly large black hole tho so be careful if you do :)

- amistre64

have you gone over how to find the terms used: a, d, n ?

- anonymous

yes

- amistre64

good, cause one you know how to get those, the rest is just simple arithmetic

- amistre64

*cause once you know

- anonymous

d common difference

- amistre64

how do you find the common difference of the sequence?

- anonymous

subtract.

- amistre64

right, subtract the first term from the second term
problem 10: 7 ,13, 19, ...
d = 13-7 = 6
right?

- anonymous

yes sirr

- amistre64

and what does the "a" in the formula refer to?

- anonymous

a refers to a term

- amistre64

yes, but there is "a" special a that we need to use in the formula itself. the FIRST term. In the problem im working thru, that would be: 7
d=6, a=7
and what does "n" mean?

- amistre64

im going to use a different but equal notation for the formula:
\[f(n)=a+d(n-1)\]
\[f(n)=7+6(n-1)\]

- amistre64

you can replace \(f(n)\) with \(a_n\) if you want, its just a placeholder

- amistre64

the "n" is reserved for the position of the term we want to find. in this case, the 90th term
\[f(n)=7+6(n-1)\]
\[f(90)=7+6(90-1)\]
\[f(90)=7+6(89)\]
\[f(90)=7+534\]
\[f(90)=541\]

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