Question 1181277
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The first term of an arithmetic sequence is 9689 and the 100th term is 8996.
a) Find the general term.
b) Find the 110th term.
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<pre>
The distance between the first term and the 100-th term is

    9689 - 8996 = 693,


and there are 99 gaps of equal length between these points on the number line.


So, each gap is  {{{693/99}}} = 7 units.


Thus the common difference of the AP is -7  (the progression decreases).


Now the general term  is   {{{a[n]}}} = {{{a[1] + (n-1)*d}}} = 9689 + (n-1)*(-7) = 9689 -7n + 7 = 9696 - 7n.    <U>ANSWER</U>


The 110-th term is  9696 - 110*7 = 8926.          <U>ANSWER</U>
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Solved.