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Question

Find the geometric series whose 5th and 8th terms are 80 and 640, respectively.


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Solution

Step 1. Find the common ratio:

Here it is given that 5th term is 80 and 8th term is 640

Let the first term is a and the common ratio isr

a5=ar4=80....(i)

a8=ar7=640....(ii)

Divide (ii) and (i)

ar7ar4=64080r3=8r=2

Step 2. Find the GP series:

Put the value of 2 in eq i

ar4=80a×24=80a=8016a=5

Second term,

ar=5×2=10

Third term

ar2=5×22=20

Fourth term

ar3=5×23=40

Therefore,the required GP is 5,10,20,40,80,..640.


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