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Question

In a GP, the 3rd term Is 24 and the 6th term Is 192 then find the 10th term.


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Solution

Step 1: Form equation using given terms of Geometric Progression

The 3rd term a3=24

And, the 6th term a6=192

As we know, the nth term of a GP is defines as,

an=arn-1

So, the 3rd term is,

a3=ar2

So, ar2=24 ...(i)

And, the 6th term is,

a6=ar5

So, ar5=192 ...(ii)

Step 2: Calculate the common ratio r

On dividing the equation (ii) by equation (i), we get,

ar5ar2=19224

r5r2=81

r5-2=8 [aman=am-n]

r3=8

r33=83 [Taking cube root on both sides]

r33=233

r=2 [ann=a]

Step 3: Calculate the first term a

Substituting the value of r in equation (ii),

ar2=24

a22=24

4a=24

a=244

a=6

Step 4: Calculate the 10th term

As we know, the nth term of a GP is defines as,

an=arn-1

So, the 10th term is,

a10=ar9

a10=629 a=3,r=2

a10=32×2×2×2×2×2×2×2×2×2

a10=3×1024

a10=3072

Hence, the 10th term of the given GP is 3072.


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