Geometric progression

In geometric progression, a1 = 7, q = 5. Find the condition for n to sum first n members is: sn≤217.

Correct result:

n =  3

Solution:

a1=7 q=5 s=217  s=aq qn1q1 s/a1 (q1)=qn1 s/a1 (q1)+1=qn lns/a1 (q1)+1=nlnq  n=ln(s/a1 (q1)+1)ln(q)=ln(217/7 (51)+1)ln(5)=3



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