Find a formula for an for the arithmetic sequence.
a2 = 93, a6 = 65
any help would be greatly appreciated. thank you.
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 $\displaystyle a_1$
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
$\displaystyle d = -14$
$\displaystyle a_1 =135$