Question

Q6. In a certain A.P. the 24th term is twice the 10th term. Prove that the 72nd term is twice the 34th term.​

Answer 1

Answer:

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Step-by-step explanation:

☞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

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Answer 2

As We know that 24th term is twice the 10th term in an AP.

→ T₂₄ = 2[T₁₀]

→ a + 23d = 2[a + 9d]

→ a + 23d = 2a + 18d

→ a = 5d ••••• [1]

Now, We've to prove that 72th term is twice as 34th term.

→ T₇₂

→ a + 71d

→ a + 5d + 66d [Using split term]

→ a + a + 66d = 2a + 66d

→ 2(a + 33d) = 2[a + (34–1)d]

→ 2[T₃₄]

Hence,

It's PROVED that 72th term is as twice as 34th term of an AP.