Insert into GP

Between numbers 5 and 640 insert as many numbers to form geometric progression so sum of the numbers you entered will be 630. How many numbers you must insert?

Correct result:

m =  6

Solution:

a1=5 an=640 sn=630+640+5=1275 an=a1qn1 sn=qn1q1  128=qn1=qn/q 1275=qn1q1  1275=5128q1q1 1275q1275=5(128q1) 635q=1270 q=2  128=qn1 ln128=(n1)ln2 n=8  m=n2=82=6



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