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In a certain A.P. 31th term is twice the 12th term. Prove that 70th term is twice the 31th term. |
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Answer» T₃₂=a+(32-1)d=a+31dwhere a=1st term and d=common difference of the A.P.t₁₂=a+(12-1)d=a+11dNow by the given condition,a+31d=2(a+11d)or, a+31d=2a+22dor, a-2a=22d-31dor, -a=-9dor, a=9dNow,t₃₁=a+(31-1)d=a+30d=9d+30d=39d∴, t₇₀=a+(70-1)d=a+69d=9d+69d=78d=2×39d=2t₃₁ (Proved) |
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