Question 1051855
Find a and b if {{{sum( ak+b, k=1, n ) = 8n^2+11n}}}, given that {{{sum( k, k=1, n ) = (n(n+1))/2}}}
<pre>
The easy way is to substitute n=1 and n=2, and not even bother
with {{{sum( k, k=1, n ) = (n(n+1))/2}}}

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Substituting n=1:

{{{sum( ak+b, k=1, 1 ) = a(1)+b=a+b=8(1)^2+11(1)=8+11=19}}}

So {{{a+b=19}}}

Substituting n=2

{{{sum( ak+b, k=1, 2 ) = a(1)+b+a(2)+b=3a+2b=8(2)^2+11(2)=8(4)+22=32+22=54}}}

So {{{3a+2b=54}}}

Solve the system:

{{{system(a+b=19,3a+2b=54)}}}

by substitution or elimination

Get a=16, b=3 

{{{sum( 16k+3, k=1, n ) = 8n^2+11n}}}

Edwin</pre></b>