Question 429783
{{{a[n]-a[n-1] = 2n-1}}} is the recursion law.
Now
{{{a[n-1]-a[n-2] = 2n-3}}},
{{{a[n-2]-a[n-3] = 2n-5}}},
....................
{{{a[3]-a[2] = 5}}},
{{{a[2]-a[1] = 3}}}.
==> {{{a[n] - a[1] = (2n - 1) + (2n - 3) + (2n - 5) }}}+ ...+ {{{5 + 3}}} by adding corresponding sides.
<==>  {{{a[n] - 8 = ((n-1)/2)*(3 + (2n-1))}}}
<==>  {{{a[n] - 8 = ((n-1)/2)*(2n + 2) = (n-1)(n+1) = n^2 - 1}}}
<==>  {{{a[n] = n^2 + 7}}}
==> {{{a[2000] = 2000^2 + 7 = 4000007}}}