Question

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

Options

• 23

• 28

• 38

• 33

Answer 1

The middle most term of the A.P. 3, 8, 13, ....., 63 is 33.

Explanation:

a = 3

d = 8 − 3

= 5

a_n = 63

a_n = a + (n − 1)d

63 = 3 + (n − 1)5

63 − 3 = (n − 1)5

60 = (n − 1)5

`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`

= `14/2`

= 7 term

a₇ = 3 + (7 − 1)5

a₇ = 3 + (6)5

a₇ = 3 + 30

a₇ = 33