Question

the 24th term of the AP is twice its 10th term. show that 72th term is 4 times the 15th term.

Answer 1

hello dear ,
so, a24 = 2 x a10
=>a + 23d = 2(a + 9d)
=>​a + 23d = 2a + 18d
=>2a-a = 23d-18d
=>a = 5d-----------(1)

now, ​RHS:-
a15 = a + 14d 
      = 5d + 14d-----------from (1)
​      = 19d-----------(1)

now, LHS:-
a72 = a + 71d
      = 5d + 71d = 76d
      = 4 x 19d 
      = 4 x a15 -----------from (2)

hope its help you dear , :-)

Answer 2

hope it will help you