The sum of an infinite G.P. is 16 and the sum of the square of its terms is 153 3/5. Find the fourth term of the progression: a. 7/16 b. 5/32 c.3/16 d. None

Let the first term of GP is a and common ratio is r, a1-r=16and a21-r2=15335=7685Squaring first equation and dividing by second we get, 1-r21-r2=16×5768=5481+r1-r=54848+48r=5-5r53r=-43r = -4353So a=16×1+4353=153653SO fourth term a4=ar3=153653×-4353×-4353×-4353So you can see that d is the correct option.

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