Find the middle t

For given AP,

First term, a = 1

Common difference, d = a₂ – a

= 8 – 1

= 7

Let the number of terms be n, then

Last term, a_n = 505

We know, nth term of an AP is

a_n = a + (n – 1)d

⇒ 505 = 1 + (n – 1)7

⇒ 504 = 7(n – 1)

⇒ n – 1 = 72

⇒ n = 73

Also,

a₃₇ = a + 36d

= 1 + 36(7)

= 1 + 252

= 253