Question 1160989
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The non-standard solution shown by tutor @ikleyn is a good one....  Here is one that is more traditional.<br>
(1) Use the given sum of the first 17 terms and the given first term to find the 17th term.<br>
{{{S[17] = 17((a[1]+a[17])/2)}}}
{{{629 = 17(((-3)+a[17])/2)}}}
{{{74 = -3+a[17]}}}
{{{a[17] = 77}}}<br>
(2) Use the 1st and 17th terms to find the common difference.<br>
{{{a[17] = a[1]+16d}}}
{{{77 = (-3)+16d}}}
{{{80 = 16d}}}
{{{d = 5}}}<br>
The common difference is 5.<br>
(3) Use the first term and the common difference to find the 29th term.<br>
{{{a[29] = a[1]+28d}}}
{{{a[29] = (-3)+28(5) = (-3)+140 = 137}}}<br>
The 29th term is 137.<br>