Question

Find the middle term of 3-digits number which is divisible by 3.​

Answer 1

Solution:-

List 3 digits number which is divisible by 3 are

102 , 105 , 108 , 111 , ................... 999

We get

$\rm \: T_n = 999$

$\rm \: first \: term \: (a) = 102$

$\rm \: common \: difference \: = a_2 - a_1 = 105 - 102 = 3$

Using this formula

$\rm \: T_n = a + (n - 1)d$

Put the value on formula

$\rm \: 999 = 102 + (n - 1)3$

$\rm \: 999 = 102 + 3n - 3$

$\rm \: 999 = 99 + 3n$

$\rm \: 3n = 999 - 99$

$\rm \: 3n \: = 900$

$\rm \: n = \frac{900}{3}$

$\rm \: n = 300$

For even nth term

$\rm \: middle \: term \: = \frac{n}{2}$

$\rm \: middle \: term \: = \frac{300}{2} = 150$

So middle term is 150