Geometric progressiob

If the sum of four consecutive terms of a geometric progression is 80 and the arithmetic mean of the second and fourth terms is 30, then find terms.

Correct answer:

a =  2
b =  6
c =  18
d =  54

Step-by-step explanation:

a+b+c+d=80 (b+d)/2 = 30 b = qa c = qb d = qc  a+c + 2 30 = 80 a+c = 20  a + aq2 = 20  a(1+q2) = 20 qa(1+q2) = 60 q=60/20=3  a=1+q220=1+3220=2
b=q a=3 2=6
c=q b=3 6=18
d=q c=3 18=54

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