Question

in a certain AP the 32nd term is twice the 12th term. prove that 70th term is twice tge 31st term

Answer 1

t₃₂=a+(32-1)d
=a+31d 
where a=1st term and d=common difference of the A.P.
t₁₂=a+(12-1)d
=a+11d
Now by the given condition,
a+31d=2(a+11d)
or, a+31d=2a+22d
or, a-2a=22d-31d
or, -a=-9d
or, a=9d
Now, t₃₁=a+(31-1)d
=a+30d
=9d+30d
=39d
∴, t₇₀=a+(70-1)d
=a+69d
=9d+69d
=78d
=2×39d
=2t₃₁ (Proved)

Answer 2

Step-by-step explanation:

please see the attachment

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