Descending 81797

The sum of the first two terms of the descending geometric sequence is five quarters, and the sum of the infinite geometric series formed from it is nine quarters. Write the first three terms of the geometric sequence.

Correct answer:

g1 =  3/4
g2 =  1/2
g3 =  1/3 = 1:3
G1 =  3.75
G2 =  -5/2
G3 =  5/3 = 5:3

Step-by-step explanation:

g1+g2=45 s=49=2.25  g1+q g1 = 45  s=1qg1  g1+q g1 = 5/4 9/4  (1q) = g1  g1(1+q) = 5/4 9/4  (1q) = g1  9/4  (1q) (1+q) = 5/4  9 (1x) (1+x)=5  9 (1x) (1+x)=5 9x2+4=0 9x24=0 x1,2=±4/9=±0.666666667 x1=0.666666667 x2=0.666666667 q<1 q=x1=0.6667=320.6667  g1=s (1q)=2.25 (10.6667)=43=0.75

Our quadratic equation calculator calculates it.

g2=q g1=0.6667 0.75=21=0.5
g3=q g2=0.6667 0.5=310.3333=1:3
Q=x2=(0.6667)=320.6667 G1=s (1Q)=2.25 (1(0.6667))=415=343=3.75
G2=Q G1=(0.6667) 3.75=25=221=2.5
G3=Q G2=(0.6667) (2.5)=35=1321.6667=5:3

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