The sum of the first 8 terms of a geometric series is 17 times the sum of its first 4 terms.  Find the common ratio.

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Let the common ratio be r1st , sum of 8 terms s8 = a(1-r^8)/(1-r)=a(1+r^4)(1-r^4)/(1-r)s4 = a(1-r^4)/(1-r)now, s8 is 17 times s4s8 = 17* s4or, a(1+r^4)(1-r^4)/(1-r) = 17 * a(1-r^4)/(1-r)or,1+r^4 = 17 or,r^4 = 17 - 1or r^4 = 16or, r^4 = 2^4thus, r = 2.which is the required answer. and check if u want to.s8= (1-2^8)/(1-2) = 255s4 = (1-2^4)/(1-2) = 15s8 = 255 = 17 * 15 = 17 * s4thus, we are correct. yipeee!!