if the ratio of the sum of the first 6 terms of a g. p. to the sum of the first 3 terms of the g. p. is 65, what is the common ratio of the g. p?
Choose the correct choice from the following:
A) 4
B) 1 / 4
C) 2
D) 9
E) 1 / 9
<gadget id="calculator">65 - 1</gadget>
<output>64</output>

<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>

<gadget id="calculator">64 ** (1/3)</gadget>
<output>4</output>

<result>A</result>
if the ratio of the sum of the first 6 terms of a g. p. to the sum of the first 3 terms of the g. p. is 65, what is the common ratio of the g. p?
power(subtract(65, const_1), divide(const_1, const_3))
65 = ( a 1 + a 2 + a 3 + a 4 + a 5 + a 6 ) / ( a 1 + a 2 + a 3 ) factorize the same terms 65 = 1 + ( a 4 + a 5 + a 6 ) / ( a 1 + a 2 + a 3 ) write every term with respect to r a 1 = a 1 a 2 = a 1 * r ^ 1 a 3 = a 1 * r ^ 2 . . . . . . . . . 65 = 1 + ( a 1 ( r ^ 3 + r ^ 4 + r ^ 5 ) ) / ( a 1 ( 1 + r ^ 1 + r ^ 2 ) ) 64 = ( r ^ 3 ( 1 + r ^ 1 + r ^ 2 ) ) / ( ( 1 + r ^ 1 + r ^ 2 ) ) 64 = r ^ 3 r = 4 a