Generally speaking, arithmetic sequences have the form:
an=a1+(n-1)*d
Where:
an=the nth term in the sequence
a1=the 1st term in the sequence
n=the number of terms in the sequence
d=the difference between consecutive terms (i.e. d=an-an-1=a2-a1=a3-a2, etc.)
The SUM of the terms of an arithmetic sequence, notated Sn, is given by:
Sn=[n/2]*[2a1+(n-1)*d]
So if n=8 then:
a8=a1+7d=63
And if there are 94 terms in the sequence then:
S94=[94/2]*[2a1+93d]=47*(2a1+93d)=94a1+4371d=1000
So this is a system of equations where:
{ a1 + 7d = 63 (Multiply this first equation by -94 on both sides and add to second equation)
{ 94a1 + 4371d = 1000
-94a1 - 658d = -5922 (Add this new equation to second equation)
Therefore:
3713d = -4922
So:
d = -4922/3713
