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

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, an = 505

We know, nth term of an AP is

an = 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

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