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The numbers `3^(2sin2alpha-1),14and3^(4-2sin2alpha)` form first three terms of A.P., its fifth term isA. `-25`B. `-12`C. 40D. 53 |
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Answer» Correct Answer - D Since,`3^(2sin2alpha-1),14and3^(4-2sin2alpha)` `:." "2xx143^(2sin2alpha-1)+3^(4-2sin2alpha)` `rArr" "28=(a)/(3)+(3^(4))/(a)`, where `a=3^(2sin2alpha)` `rArr" "a^(2)-84a+243=0` `rArr" "(a-81)(a-3)=0` `rArr" "a=81,a=3` `rArr" "3^(2sin2alpha)=3^(4)or,3^(2sin2alpha)=3` `rArr" "2sin2alpha=1" "[because2sin2alpha!=4]` `rArr" "sin2alpha=(1)/(2)rArr2alpha=(pi)/(6)` Thus, the first three terms of the A.P. are 1,14,27. Hence, its fifth term is 53. |
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