Question

The 24 term of an A.P. is twice its
10th term show that its 72 term
is 4 times its 15th term.
​

Answer 1

Answer:

Given:

24th term of an A.P is twice it's 10th term

To prove:

72nd term is 4 times it's 15th term

Step-by-step explanation:

Considerd a to be the 1st term and d to be the common difference of an A.P.

From given,

a24=2a10......(1)

We know that,

an=a+(n-1)d.......(2)

Thus, a24=a+23d and a10=a+9d

substitute the value of a24 and a10 in equation (1), we get

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

a+23d=2a+18d

Now, shift the terms to right hand side and keep the d term in left hand side, we get

23-18d=2a-a

a=5d

Now, from question

a72/a15=a+71d/a+14d

Now, substitute the value of a=5in above equation, we get

a72/a15=76d/19d

a72/a15=4

a72=4(a15)

Therefore, the 72nd term is 14 times the 15th term,

Hence proved

Answer 2

Answer:

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