Question 1092278
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Using a for the first term and d for the common difference...<br>
S(2) = a + (a+d) = 2a+d = 10<br>
S(10) = a + (a+d) + (a+2d) + ... + (a+9d) = 10a+45d<br>
So we know
{{{2a+d = 10}}}
{{{10a+45d = 2}}}<br>
Multiply the first equation by 5 and subtract the second equation to eliminate variable a, then solve for d.<br>
{{{10a+5d = 50}}}
{{{40d = -48}}}
{{{d = -48/40 = -1.2}}}<br>
The common difference, d, is -1.2.  Plug this value into one of the earlier equations to solve for a.<br>
{{{2a+(-1.2) = 10}}}
{{{2a = 11.2}}}
{{{a = 5.6}}}<br>
The first term, a is 5.6.<br>
Answers: first term is 5.6; common difference is -1.2.