Question

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

Answer 1

Given below is the answer to your question.....

Answer 2

$\Large{\textbf{\underline{\underline{According\:to\:the\:Question}}}}$

${\boxed{\sf\:{t_{n}=a+(n-1)d}}}$

$\tt{\rightarrow t_{32}=a+(32-1)d}$

= a + 31d

First term = a

Common difference = d

$\tt{\rightarrow t_{21}=a+(12-1)d}$

=a + (12 - 1)d

= a + 11d

Situation

a + 31d = 2(a + 11d)

a + 31d = 2a + 22d

a - 2a = 22d - 31d

-a = -9d

a = 9d

Hence,

$\tt{\rightarrow t_{31}=a+(31-1)d}$

= a + 30d

= 9d + 30d

= 39d

$\tt{\rightarrow t_{70}=a+(70-1)d}$

= a + 69d

= 9d + 69d

=78d

Hence we get :-

= 2 × 39d

=2t₃₁

${\boxed{\sf\:{2t_{31}}}}$