Question 1163035
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With first term a and common ratio r....<br>
the sum of the first two terms is {{{a+ar}}};
the infinite sum is {{{a/(1-r)}}}<br>
The condition is that the infinite sum be twice the sum of the first two terms:<br>
{{{a/(1-r) = 2(a+ar)}}}
{{{1/(1-r) = 2(1+r)}}}
{{{1/2 = 1-r^2}}}
{{{r^2 = 1/2}}}
{{{r = sqrt(2)/2}}} or {{{r = -sqrt(2)/2}}}<br>
Both solutions satisfy the condition of the problem.<br>
ANSWER: The possible common ratios are {{{sqrt(2)/2}}} and {{{-sqrt(2)/2}}}<br>