Question

Find the middle term of A.P 1,8,15.......505

Answer 1

505=1+(n-1)7
505=1+7n-7
505=7n-6
511=7n
n=73
middle term=73+1/2
=37
hence the term is
1+(37-1)7
253

Answer 2

In given AP,

1 , 8 , 15 ......... , 505

Here, a = 1

d = 8 - 1 = 7

An = 505

An = a + ( n-1 ) d

505 = 1 + ( n-1 ) 7

505 - 1 = ( n-1 ) 7

504 / 7 = ( n-1)

n - 1 = 72

n = 72 + 1

n = 73

Middle term = 73 / 2 = 36.5

It is not possible.

So , a36 or a 37 is the middle most term.

a36 = a + 35d

a36 = 1 + 35(7)

a36 = 1 + 245

a36 = 246

a37 = a + 36d

a37 = 1 + 36(7)

a37 = 1 + 252

a37 = 253