Sequences, Series, and Probability

**thepride** · September 26th 2009, 11:32 AM

Find a formula for an for the arithmetic sequence.

a2 = 93, a6 = 65

any help would be greatly appreciated. thank you.

**skeeter** · September 26th 2009, 11:41 AM

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?

**thepride** · September 26th 2009, 11:48 AM

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?

**skeeter** · September 26th 2009, 12:04 PM

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.

**flexus** · September 26th 2009, 12:28 PM

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.

**skeeter** · September 26th 2009, 12:36 PM

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?

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

$a_2 = 93$ ...

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

$a_6 = 65$ ...

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

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

**flexus** · September 26th 2009, 01:07 PM

Originally Posted by skeeter

two people involved w/ this problem?

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

$a_2 = 93$ ...

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

$a_6 = 65$ ...

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

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

no i was just helping him/her out.

**flexus** · September 26th 2009, 01:11 PM

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

**e^(i*pi)** · September 26th 2009, 01:53 PM

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

$<br /> 65 = a_1 + (6-1)d<br />$

is equal to

$a_1 = 65-5d$

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

I get

$d = -14$

$a_1 =135$

**thepride** · September 26th 2009, 10:18 PM

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 $a_2 > a_6$
Hint:

$<br /> 65 = a_1 + (6-1)d<br />$

is equal to

$a_1 = 65-5d$

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

I get

$d = -14$

$a_1 =135$

thats not right i check the back of the book and the answer is An= -7n+107

can someone help me understand this problem???

**mathaddict** · September 26th 2009, 10:23 PM

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

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

and

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

Then solving the simultaneous equatino would give

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

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

=the given answer .

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