Find the value of the middle most term (s) of the AP : –11, –7, �

1.	Find the value of the middle most term (s) of the AP : –11, –7, –3,..., 49.
Answer» Here, a = –11, d = –7 – (–11) = 4, a_n = 49 We have an = a + (n – 1) d So, 49 = –11 + (n – 1) × 4 i.e., 60 = (n – 1) × 4 i.e., n = 16 As n is an even number, there will be two middle terms which are 16/2th and (16/2 + 1)th, i.e., the 8th term and the 9th term. a₈ = a + 7d = –11 + 7 × 4 = 17 a₉ = a + 8d = –11 + 8 × 4 = 21 So, the values of the two middle most terms are 17 and 21, respectively.

Find the value of the middle most term (s) of the AP : –11, –7, –3,..., 49.

Answer»

Here, a = –11, d = –7 – (–11) = 4, a_n = 49

We have an = a + (n – 1) d

So, 49 = –11 + (n – 1) × 4

i.e., 60 = (n – 1) × 4

i.e., n = 16

As n is an even number, there will be two middle terms which are 16/2th and (16/2 + 1)th, i.e., the 8th term and the 9th term.

a₈ = a + 7d = –11 + 7 × 4 = 17

a₉ = a + 8d = –11 + 8 × 4 = 21

So, the values of the two middle most terms are 17 and 21, respectively.