The middle most term of the A.P. 3, 8, 13, ....., 63 is ______.

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The middle most term of the A.P. 3, 8, 13, ....., 63 is 33. Explanation: a = 3 d = 8 − 3 = 5 an = 63 an = a + (n − 1)d 63 = 3 + (n − 1)5 63 − 3 = (n − 1)5 60 = (n − 1)5 $\frac{60}{5}$ = n − 1 12 = n − 1 12 + 1 = n n = 13 Since n = 13 (an odd number), the middle term is at the position: Middle term = (n + 1)/2 = (13 + 1)/2 = $\frac{14}{2}$ = 7 term a7 = 3 + (7 − 1)5 a7 = 3 + (6)5 a7 = 3 + 30 a7 = 33

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