Question

in an ap the 24thterm is twicethe 10th term.prove that the 36th term is twice the 16th term.

Answer 1

According to the question,

24th term = 2( 10th term )

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

a + 23d = 2a + 18d

23d - 18d = 2a - a

5d = a ----1equation

Hence,

To Prove : 36th term = 2( 16 th term )

RHS = 2 ( a + 15 d )

= 2a + 30d

= 2( 5d ) + 30d

= 10d + 30d

= 40d

LHS = 36th term

= a + 35d

= 5d + 35d

= 40d

40d = 40d

RHS = LHS

PROVED.

Answer 2

The general form of an AP is a+(n-1)d.

Given,

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

a+23d = 2a + 18d

a = 5d..

now we have to prove that 36th term is twice the 16th term.

a+35d

= 5d+35d

= 40d

= 2 × 20d

= 2(5d + 15d)

= 2(a + 15d)

= 2[a+(16-1)d]

= 2[16th term of the AP]

Hence Proved...