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 the value of c.

Correct answer:

c1 =  2
c2 =  0.3333

Step-by-step explanation:

a2=24 a3 = 12(c+1)  q = a3/a2 = 12(c+1)/24 = (c+1)/2  a1 = a2/q = 24 2/(c+1) = 48/(c+1)  s = a1+a2+a3 = 76  48/(c+1) + 24 + 12(c+1)=76  48+24(c+1)+12(c+1)2=76(c+1)  12c228c+8=0 12=223 28=227 8=23 GCD(12,28,8)=22=4  3c27c+2=0  p=3;q=7;r=2 D=q24pr=72432=25 D>0  c1,2=2pq±D=67±25 c1,2=67±5 c1,2=1.166667±0.833333 c1=2 c2=0.333333333  c=c1=2 q=(c+1)/2=(2+1)/2=23=121=1.5 a1=a2/q=24/1.5=16 a3=a2 q=24 1.5=36 s2=a1+a2+a3=16+24+36=76  s2=s  c1=2

Our quadratic equation calculator calculates it.

q=(c2+1)/2=(0.3333+1)/2=320.6667 a11=a2/q=24/0.6667=36 a33=a2 q=24 0.6667=16 s3=a11+a2+a33=36+24+16=76 s3=s2=s c2=0.3333

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