Question

the 4th term of an ap is zero prove that its 25th term is triple its 11th term

Answer 1

Hope it will help you!!

Answer 2

Hey there !

Solution:

Given : $a_4 = 0$

To prove that : $a_{25} = 3 ( a_{11} )$

Proof:

$a_4 = a + 3d$

=> $a + 3d = 0$

=> $a = - 3d$ => Equation 1

Now, $a_{11} = a + 10d$ => Equation 2

Substitute the value of a from Equation 1 in Equation 2

=> $a_{11} = - 3d + 10d$

=> $a_{11} = 7d$

$a_{25} = a + 24d$ => Equation 3

Now Substitute value of a from Equation 1 in Equation 3.

=> $a_{25} = - 3d + 24d$

=> $a_{25} = 21d$

Now comparing $a_{11}$ and $a_{25}$ we get,

7d and 21d

=> If $a_{11}$ is multiplied 3 times we get $a_{25}$

=> $a_{25} = 3 ( a_{11} )$

Hence proved.

Hope my answer helped !