Question

find the middle most term of the AP -5/4,-1,-3/4,.....,17/4​

Answer 1

Answer :

3/2

Formula used :

nth term of an AP :

a_n = a + (n - 1)d

Solution :

Given,

AP : -5/4, -1, -3/4, ... , 17/4

Here,

First term, a = -5/4

common difference, d = -1 - (-5/4)

= 1/4

Firstly to find the middle term of AP, we have to know the number of terms in it

last term, a_n = 17/4

a_n = a + (n - 1)d

17/4 = -5/4 + (n - 1)1/4

22/4 = (n - 1) 1/4

→ n = 23

Middle term = (23 + 1)/2 = 12

a_12 = a + (n - 1)d

a_12 = -5/4 + (12 - 1)1/4

→ a_12 = 6/4 = 3/2

Therefore,

Middle most term of given AP = 3/2