# 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

Correct result:

c1 =  2
c2 =  0.333

#### Solution:

Checkout calculation with our calculator of quadratic equations.

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

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