Question

Find the middle term of the AP 10, 7, 4, ……., (-62).

Answer 1

The given AP is 10,7,4,.....,-62.
First term, a = 10
Common difference, d = 7 -10 =-3
Suppose these are n terms in the given AP. Then,

a_n = -62

⇒10+ (n-1) × (-3) = -62                          [ a_n = a + (n-1) d]

⇒ -3  (n-1) =-62 -10 = -72

⇒${\displaystyle n-1=\frac{72}{3}=24}$

⇒ n = 24 + 1= 25

Thus, the given AP contains 25 terms.
∴ Middle term of the given AP

=${\displaystyle \left(\frac{25+1}{2}\right)}$ th term 

= 13 th term 

= 10+ (13-1) × (-3)

= 10-36 

=-26 

Hence, the middle term of the given AP is - 26.