# Thread: Formula for Arithmetic sequence

1. ## Formula for Arithmetic sequence

find the formula for an for the arithmetic sequence.

a3=94, a6=85

ok i know how to solve a similar problem when i am given a1 and d. but i dont have either A1 or d so how can i find them? to plug into an=dn+c and c= a1-d?? please help me understand this thank you.

2. Originally Posted by flexus
find the formula for an for the arithmetic sequence.

a3=94, a6=85

ok i know how to solve a similar problem when i am given a1 and d. but i dont have either A1 or d so how can i find them? to plug into an=dn+c and c= a1-d?? please help me understand this thank you.

HI

a+2d=94 --- 1

a+5d=85 --- 2

Solve for a and d then plug into the general equation of Ap

HI

a+2d=94 --- 1

a+5d=85 --- 2

Solve for a and d then plug into the general equation of Ap
i don't understand where you got that from. could you explain to me what this all means. im sorry i am just a little behind on all this stuff. im looking for A1 and d.

4. Originally Posted by flexus
i don't understand where you got that from. could you explain to me what this all means. im sorry i am just a little behind on all this stuff. im looking for A1 and d.
Well , look at the general form for AP

$T_n=a+(n-1)d$

So $T_2=a+(2-1)d\Rightarrow a+d$

$
T_6=a+(6-1)d\Rightarrow a+5d
$

HI

a+2d=94 --- 1

a+5d=85 --- 2

Solve for a and d then plug into the general equation of Ap

i don't know what you did but it made no sense to me. i actually figured it out. what i did was

a6-a3= 3 terms apart

a6=a3+3d--> 85=94+3d--> d=-3

an=a1+(n-1)d
94=a1+(3-1)-3-->a1=100

c=a1-d-->c=100-(-3)-->c=103

thank you very much for your time and help mathaddict! it was greatly Appreciated.

6. Originally Posted by flexus
i don't know what you did but it made no sense to me. i actually figured it out. what i did was

a6-a3= 3 terms apart

a6=a3+3d--> 85=94+3d--> d=-3

an=a1+(n-1)d
94=a1+(3-1)-3-->a1=100

c=a1-d-->c=100-(-3)-->c=103

OK , your method works fine too .. Then you stick to your method to make things easier .

### an arithmetic sequence has a 3= 94 and a6= 85 ). Determine a25

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