The r-th- s-th- and t-th- terms of a certain G-P- are R- S and T respectively- then the value of R-s-t- S-t-r- T-r-s- is-01-12

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Toppr Admin · Accepted Answer

Let the common ratio be taken as k and a be the first term-R-akr-x2212-1-x2234-Rs-x2212-t-as-x2212-tk-r-x2212-1-s-x2212-t- similarlySt-x2212-r-at-x2212-rk-s-x2212-1-t-x2212-r-Tr-x2212-s-ar-x2212-sk-t-x2212-1-r-x2212-s-Multiplying the above three and knowing that-x2234-Rs-x2212-tSt-x2212-rTr-x2212-s-a0-k0-1

The rth, sth and tth terms of a certain G.P. are R, S and T respectively, then the value of Rs−tSt−rTr−s is-01-12

Let the common ratio be taken as k and a be the first term.R=akr−1∴Rs−t=as−tk(r−1)(s−t) similarlySt−r=at−rk(s−1)(t−r)Tr−s=ar−sk(t−1)(r−s)Multiplying the above three and knowing that∴Rs−tSt−rTr−s=a0.k0=1

The $r^{t h}$ , $s^{t h}$ and $t^{t h}$ terms of a certain G.P. are R, S and T respectively, then the value of $R^{s - t} S^{t - r} T^{r - s}$ is-
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