Question 964283
1)The sum of the first 13 terms in arithmetic sequence is 1,475.5 
<pre>
n=13, S<sub>13</sub>=1475.5

Substitute in the sum formula:

{{{S[n]=expr(n/2)(2a[1]+(n-1)^""d)}}}
{{{S[13]=expr(13/2)(2a[1]+(13-1)^""d)}}}
{{{1475.5=expr(13/2)(2a[1]+(12)^""d)}}}
Multiply both sides by 2:
{{{2951=13(2a[1]+12d)}}}
Divide both sides by 13
{{{227=2a[1]+12d}}}
</pre>
131 is known to be the 8th term. Find the first term and common difference of this sequence?
<pre>
----
n=8, a<sub>8</sub>=131

Substitute in the nth term formula:

{{{a[n]=a[1]+(n-1)d}}}
{{{a[8]=a[1]+(8-1)^""d)}}}
{{{131=a[1]+7d)}}}

That gives us a system of two equations in two unknowns:

{{{system(227=2a[1]+12d,131=a[1]+7d)}}}

Solve that system by substitution or elimination and you'll
get the answer.  You do that by yourself.

Edwin</pre>