Two geometric progressions

Insert several numbers between numbers 6 and 384 so that they form with the given GP numbers and that the following applies:
a) the sum of all numbers is 510

And for another GP to apply:

b) the sum of entered numbers is -132
(These are two different geometric sequences but with the same two members)

Final Answer:

n =  4
q =  4
n2 =  7
q2 =  -2

Step-by-step explanation:

a1=6 an=384 sn=510  sn = a1   q1qn1 an = a1   qn/q  sn = a1   q1an/a1 q1  sn (q1)=a1 (an/a1 q1) 510 (q1)=6 (384/6 q1)  756q=3024  q=7563024=4  q=4  n=log(an/a1 q)/logq=log(384/6 4)/log4=4



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