Question

find value of middle term of Ap -6,-2,2,.....58

Answer 1

-6,-2,2,.....58

a= -6 , d=4
l=58
a+(n-1)d=58
on solving....
n=17

middle term = (n+1/2)th term = 9 th term

therefore , middle term = 9 th term = a+8d = - 6 + 8(4) = - 6 +32 =26

Answer 2

Given:

-6,-2,2,...58

To Find:

Find the value of the middle term of the AP

Solution:

Arithmetic Progression is a progression in which the consecutive terms differs by a common difference which is the same for every term in the series, the common difference is denoted by d and the first term is denoted by a,

The basic equation of the nth term of AP will be,

$T_n=a+(n-1)d$

So now the

first term a=-6

common difference= -2-(-6)

                              d=4

So the last term of the following AP is 58, now

58=-6+(n-1)4

64=(n-1)4

16=n-1

n=17

So there are a total of 17 terms in the AP,

The Middle term will be,

[tex]=\frac{17+1}{2} \\ =9th[/tex]

So the middle term is the 9th term, which will be equal to,

[tex]T_9=-6+(9-1)4\\ =-6+32\\ =26[/tex]

Hence, the value of the middle term is 26.