Question

In a
certains AP 32nd term is twice
the 12th term. prove that 70 th
term is all twice the 31st
term​

Answer 1

Answer:

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

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