Question

Given two terms in an arithmetic sequence find the explicit formula for a17=-95 and a38=-200

Answer 1

Answer:

$a_{n} = -15-5(n-1)$

Step-by-step explanation:

There are two things necessary for determining the general formula of an arithmetic sequence: the first term and the common difference. So we need two equations to work out two variables. Let's use the first piece of information to form the first equation

$a_{17}  = a_{1} + d(17-1)\\-95 = a_{1} +16d  .........(1)$

Now let's repeat the step above to find the second equation

$a_{38} = a_{1}+d(38-1)\\-200 = a_{1} +37d$

Solving for the two equations simultaneously

we find that a1 = -15 and d = -5