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)  48+24(c+1)+12(c+1)2=76(c+1) 12c228c+8=0  p=12;q=28;r=8 D=q24pr=2824128=400 D>0  c1,2=q±D2p=28±40024 c1,2=28±2024 c1,2=1.16666667±0.833333333333 c1=2 c2=0.333333333333   Factored form of the equation:  12(c2)(c0.333333333333)=0  c=c1=2 q=(c+1)/2=(2+1)/2=32=112=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=230.6667 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=13

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