# GP - three members

The second and third of a geometric progression are 24 and 12(c+1) respectively, given that the sum of the first three terms of progression is 76 determine value of c

Result

c1 =  2
c2 =  0.333

#### Solution:

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$q = (c_{ 2 }+1)/2 = (0.3333+1)/2 = \dfrac{ 2 }{ 3 } \doteq 0.6667 \ \\ a_{ 11 } = a_{ 2 }/q = 24/0.6667 = 36 \ \\ a_{ 33 } = a_{ 2 } \cdot \ q = 24 \cdot \ 0.6667 = 16 \ \\ s_{ 3 } = a_{ 11 }+a_{ 2 }+a_{ 33 } = 36+24+16 = 76 \ \\ s_{ 3 } = s_{ 2 } = s \ \\ c_{ 2 } = 0.3333 = \dfrac{ 1 }{ 3 } \doteq 0.3333 = 0.333$

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