Question 754041
Q:
x+3, x-15, 24 are the first 3 terms to a geometric sequence, find the values of x.
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A:
Common ratio, r = {{{(x - 15)/(x + 3)}}} = {{{24/(x - 15)}}}, cross-multiply
{{{(x - 15)^2}}} = {{{24(x + 3)}}}
{{{x^2 - 30x + 225}}} = {{{24x + 72}}}
{{{x^2 - 54x + 153 =  0}}}
{{{(x - 51)(x - 3) = 0}}}
x - 51 = 0 or x - 3 = 0
x = {{{highlight(51)}}} OR {{{highlight(3)}}}