# Thread: Sequences, Series, and Probability

1. ## Sequences, Series, and Probability

Find a formula for an for the arithmetic sequence.

a2 = 93, a6 = 65

any help would be greatly appreciated. thank you.

2. Originally Posted by thepride
Find a formula for an for the arithmetic sequence.

a2 = 93, a6 = 65

any help would be greatly appreciated. thank you.
what is the formula for the nth term of an arithmetic sequence?

3. Originally Posted by skeeter
what is the formula for the nth term of an arithmetic sequence?
im pretty sure its an = dn + c

but what do i do??? i missed classed and my professor doesnt work on the weekends?

4. Originally Posted by thepride
im pretty sure its an = dn + c
better look it up and make sure ... you'll need it to solve this problem.

5. Originally Posted by skeeter
better look it up and make sure ... you'll need it to solve this problem.
ok i found this an= dn + c this is linear form

and i also found this an= a1 +(n -1)d this is alternative form. hope this helps.

6. Originally Posted by flexus
ok i found this an= dn + c this is linear form

and i also found this an= a1 +(n -1)d this is alternative form. hope this helps.
two people involved w/ this problem?

$\displaystyle a_n = a_1 + (n-1)d$

$\displaystyle a_2 = 93$ ...

*** $\displaystyle 93 = a_1 + (2-1)d$

$\displaystyle a_6 = 65$ ...

*** $\displaystyle 65 = a_1 + (6-1)d$

you have two equations (***) with two unknowns ... solve the system for $\displaystyle d$ and $\displaystyle a_1$

7. Originally Posted by skeeter
two people involved w/ this problem?

$\displaystyle a_n = a_1 + (n-1)d$

$\displaystyle a_2 = 93$ ...

*** $\displaystyle 93 = a_1 + (2-1)d$

$\displaystyle a_6 = 65$ ...

*** $\displaystyle 65 = a_1 + (6-1)d$

you have two equations (***) with two unknowns ... solve the system for $\displaystyle d$ and $\displaystyle a_1$
no i was just helping him/her out.

8. ## Binomial Theorem

good luck trying to solve that one thepride. i have no clue.

9. These are two linear equations so should be relatively simple to solve. Already I can see that the common difference will be negative because $\displaystyle a_2 > a_6$
Hint:

$\displaystyle 65 = a_1 + (6-1)d$

is equal to

$\displaystyle a_1 = 65-5d$

-------------

I get

$\displaystyle d = -14$

$\displaystyle a_1 =135$

10. Originally Posted by e^(i*pi)
These are two linear equations so should be relatively simple to solve. Already I can see that the common difference will be negative because $\displaystyle a_2 > a_6$
Hint:

$\displaystyle 65 = a_1 + (6-1)d$

is equal to

$\displaystyle a_1 = 65-5d$

-------------

I get

$\displaystyle d = -14$

$\displaystyle a_1 =135$
thats not right i check the back of the book and the answer is An= -7n+107

can someone help me understand this problem???

11. Originally Posted by thepride
thats not right i check the back of the book and the answer is An= -7n+107

can someone help me understand this problem???

HI

we know that

$\displaystyle a_2=93 \Rightarrow a+d=93$ ---- 1

and

$\displaystyle a_6=65 \Rightarrow a+5d=65$ ----2

Then solving the simultaneous equatino would give

$\displaystyle d=-7$ and $\displaystyle a=100$

$\displaystyle T_n=100+(n-1)(-7)$