Question

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

Answer 1

Answer:

Step-by-step explanation:

Given :  

a24 = 2(a10)

By using the formula , 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 - 2a - 18d + 23d = 0

-a + 5d = 0

a - 5d = 0

a = 5d ……….(1)

We have to prove that : a72 = 4( a15)

a + (72 - 1)d = 4 (a + (15 - 1)d)

a + 71d = 4(a + 14d)

5d + 71d = 4(5d + 14d)

[from eq 1]

76d = 4(19d)

Therefore, a72 = 4( a15)

Hence proved.  

HOPE THIS ANSWER WILL HELP YOU...

Answer 2

Step-by-step explanation:

hope it is helpful to you