Question 978199
ARITHMETIC SERIES - Sn=n/2(a1 + an)

Find the sum of the terms of the following arithmetic sequences.
1, 4/3, 5/3, 2,..., a10 (a, sub 10)
<pre>
To find the common difference:

{{{d}}}{{{""=""}}}{{{matrix(1,5,2nd,term,""-"",1st,term)}}}{{{""=""}}}{{{matrix(1,5,3rd,term,""-"",2nd,term)}}}{{{""=""}}}{{{matrix(1,5,4th,term,""-"",3rd,term)}}}{{{""=""}}}

{{{d}}}{{{""=""}}}{{{4/3-1}}}{{{""=""}}}{{{4/3-3/3}}}{{{""=""}}}{{{1/3}}}
{{{d}}}{{{""=""}}}{{{5/3-4/3}}}{{{""=""}}}{{{1/3}}}
{{{d}}}{{{""=""}}}{{{2-5/3}}}{{{""=""}}}{{{6/3-5/3}}}{{{""=""}}}{{{1/3}}}

{{{a[n]=a[1] + (n-1)d}}} 

Substitute 10 for n:

{{{a[10]=a[1] + (10-1)(1/3)}}}

Substitute 1 for a<sub>1</sub> and calculate a<sub>1</sub>.

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{{{s[n] = expr(n/2)(a[1]+a[n])}}}

Substitute 10 for n:

{{{s[10] = expr(10/2)(a[1]+a[10])}}}

Substitute 1 for a<sub>1</sub> and what you got in the 
first part for a<sub>10</sub>

Edwin</pre>