Question

Which term of the GP.
i) 2,8,32,.... is 512 ?
ii) √3,3,3√3.... is 729 ?
iii) 1/3,1/9,1/27.... is 1/2187 ?​

Answer 1

Answer:

i)5, ii)7 and iii)7

Step-by-step explanation:

i)a=t1=2,t2=8,t3=32 and tn=512

so, r=4

tn=ar^n-1

512=2*4^n-1

4^n-1=512/2

4^n-1=256

4^n-1=4⁴

so, n-1=4

n=5

ii) a=t1=√3,t2=3,t3=3√3,tn=729

so, r=√3

tn=ar^n-1

729=√3*√3^n-1

√3^n-1=729/√3

3^n-1=729

3^n-1=3^6

so, n-1=6

n=7

iii)a=t1=1/3,t2=1/9,t3=1/27,tn=1/2187

so, r=1/3

tn=ar^n-1

1/2187=1/3*1/3^n-1

1/3^n-1=1/2187÷1/3

1/3^n-1=1/2187*3

1/3^n-1=1/729

so, 3^n-1=729......(1&1 get cancelled)

3^n-1=3^6

so, n-1=6

n=7

Hope it will help you.

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