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Question -

Find the 4th term from the end of the G.P. ½, 1/6, 1/18, 1/54, … , 1/4374



Answer -

The nth term from theend is given by:

an = l(1/r)n-1 where, l is the last term, r is the common ratio, n isthe nth term

Given: last term, l =1/4374

r = t2/t1 =(1/6) / (1/2)

= 1/6 × 2/1

= 1/3

n = 4

So, an =l (1/r)n-1

a4 =1/4374 (1/(1/3))4-1

= 1/4374 (3/1)3

= 1/4374 × 33

= 1/4374 × 27

= 1/162

 4th termfrom last is 1/162.

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