Question 927791

Find the 1st term of the arithmetic sequence with 11th term −1 and 21th term 7.
<pre><font face = "Tohoma" size = 4 color = "indigo"><b>{{{t[n] = t[1] + (n - 1)d}}}
{{{t[11] = t[1] + (11 - 1)d}}} 
{{{- 1 = t[1] + 10d}}}
{{{10d = - t[1] - 1}}}______{{{d = (- t[1] - 1)/10}}} ---------- eq (i)

{{{t[n] = t[1] + (n - 1)d}}}
{{{t[21] = t[1] + (21 - 1)d}}}
{{{7 = t[1] + 20d}}}
{{{t[1] + 20d = 7}}} ------- eq (ii) 
{{{t[1] + 20((- t[1] - 1)/10) = 7}}} ------- Substituting {{{(- t[1] - 1)/10}}} for d in eq (ii)
{{{t[1] + 2(- t[1] - 1) = 7 }}}
{{{t[1] - 2t[1] - 2 = 7}}} 
{{{- t[1] = 7 + 2}}}
{{{- t[1] = 9}}}
Term 1 or {{{t[1] = 9/(- 1)}}}, or {{{highlight_green(t[1] = - 9)}}} 
You can do the check!! 
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