Question 1106995
If x is first term, and d the common difference, the sum to 16, when simplifed gives {{{2x+3d=8}}}.


Squares-description gives  {{{(x+3d)^2=x^2+48}}}.


Solve the system for d and x.
Substituting for 3d,
{{{(x+8-2x)^2=x^2+48}}}
{{{(8-x)^2=x^2+48}}}

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{{{highlight(x=1)}}}, the FIRST term of the progression.


Returning to {{{3d=8-2x}}}
{{{3d=8-2*1=6}}}
{{{3d=6}}}
{{{highlight(d=2)}}}, common difference between successive terms.

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<pre>1,  3,  5,  7</pre>