Question

if 24th term of an A.P. is twice the 10th term, prove that 72th term is twice the 34th term​

Answer 1

Step-by-step explanation:

Given that 24th term(t24) is twice the 10th term(t10). Given that 72nd term(t72) is twice the 34th term. From (1) and (2), LHS = RHS.

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Answer 2

24th term is twice the 10th term.

We know that, nth term an = a + (n – 1)d

⇒ a24 = 2(a10)

a + (24 – 1)d = 2(a + (10 – 1)d)

a + 23d = 2(a + 9d)

a + 23d = 2a + 18d

a = 5d …. (1)

Now, the 72nd term can be expressed as

a72 = a + (72 – 1)d

= a + 71d

= a + 5d + 66d

= a + a + 66d [using (1)]

= 2(a + 33d)

= 2(a + (34 – 1)d)

= 2(a34)

⇒ a72 = 2(a34)

Hence, the 72nd term is twice the 34th term of the given A.P.