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

Solve with all steps

@ajay sharma has given the correct answer. Good attempt..!

Here is the explanation.

A.P. : 1, 8, 15, .......... 505

Here, a = a₁ = 1, a₂ = 8, a₃ = 15

d = a₂ – a₁= 8 –1 = 7

Let n^th term of an A.P (a_n) be 505

i.e.  a_n = 505

⇒ a + ( n – 1)d = 505

⇒ 1 + ( n – 1) 7 = 505

⇒ 1 + 7n – 7 = 505

⇒ 7n – 6 = 505

⇒ 7n = 505 + 6

⇒ 7n = 511

⇒ n =

Thus, there are 73 terms in the A.P. (i.e. odd number of terms).

Now, middle term

 = 37^th term

 = a₃₇

 = a + ( 37 – 1)d

 = 1 + 36 × 7

 = 1 + 252

 = 253

Hence, middle term of the given A.P. is 253.