Question 1135595
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Let the first term be a and the common ratio be r.  Then<br>
(1) ar = 11  the second term is 11
(2) a/(1-r) = 100  the infinite sum is 100<br>
Solve (1) for either variable and substitute in (2)<br>
{{{(11/r)/(1-r) = 100}}}
{{{11/r = 100(1-r) = 100-100r}}}
{{{11 = 100r-100r^2}}}
{{{100r^2-100r+11 = 0}}}<br>
This is a quadratic equation that does not factor, so it has ugly irrational roots; but solving it using the quadratic formula will lead to the two solutions to the problem.