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Mathematics

If the first term, common ratio and the last term of a G.P. are a, r and l respectively, then the nth term from the end of the G.P. is given by :

  1. lrn - 1

  2. lr1 - n

  3. lr1−n\dfrac{l}{r^{1 - n}}

  4. lrn+1\dfrac{l}{r^{n + 1}}

G.P.

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Answer

When the G.P. is reversed, the first term becomes l and the new common ratio is the reciprocal of the original common ratio i.e. 1r\dfrac{1}{r}.

∴Tn=l×(1r)n−1=lrn−1=lr−(n−1)=lr1−n.\therefore T_n = l \times \Big(\dfrac{1}{r}\Big)^{n - 1} \\[1em] = \dfrac{l}{r^{n - 1}} \\[1em] = lr^{-(n - 1)} \\[1em] = lr^{1 - n}.

Hence, option 2 is the correct option.

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