Question

Find the middle term of the A.P.
-4, -2, ......... 88

Answer 1

Here, A.P.: -4,-2,.................,88

So, First term (a) = -4

Common difference (d) = -2-(-4)

                                       = 2

We know that

an = a+(n-1)d

So, 88 = (-4)+(n-1)(2)

=> 92 = 2n - 2

=> 94 = 2n

∴ n = 47

There are 47 terms so middle term would be (47+1)/2

 = 48/2 = 24

So, a₂₄ = a+(24-1)d

           = -4 + 23(2)

           = -4 + 46

           = 42

So, the middle term is 42.

Thanks!!!

Answer 2

The middle term of AP is 42.

Given :

• $- 4, \: - 2, \: ..... \: ,88$

To find:

• Find the middle term of the A.P.

Solution:

Concept/Formula to be used:

• General term of the AP: $\bf a_n= a+(n-1) d$

Step 1:

Find number of terms of given AP.

Here,

$a = - 4$

$d = 2$

$a_n= 88$

So,

$88 = - 4 + (n - 1)2$

$88 + 4 = 2(n - 1)$

$n - 1 = \frac{92}{2}$

$n - 1 = 46$

$\bf n = 47$

Step 2:

Find the middle term of AP.

Total terms of AP are 47.

So, middle term is $\frac{47 + 1}{2}$

$= 24$

Thus,

24th term is middle term of AP.

Step 3:

Calculate the 24th term.

$a_{24} = - 4 + (24-1) \times 2)$

$a_{24} = - 4 + (23 \times 2)$

$a_{24} = - 4 + 46$

$\bf a_{24} = 42$

Thus,

The middle term of AP is 42.

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