Q4 of 24 Page 115

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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