Q. 383.8( 15 Votes )

# The 24th term of

Answer :

Let a be the first term and d be the common difference.

Given: a24 = 2(a10)

To prove: a72 = 4 × a15

Now, Consider a24 = 2a10

a + 23d = 2[a + 9d]

a + 23d = 2a + 18d

a = 5d …………………. (1)

Consider a72 = a + (72 - 1)d

a72 = 5d + 71d (from equation (1))

a72 = 76d ………………. (2)

Now, consider a15 = a + (15 - 1)d

a15 =5d + 14d (from equation (1))

a18 = 19d ………………….(3)

From equation (2) and (3), we get,

a72 = 4 × a15

Hence, proved.

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