Question

Find the middle term of the A.P : -4 , -2 , 0 ......... 88

Answer 1

a= -4
d= 2
an= 88
an = a+(n-1)d
88= -4+(n-1)2
88+4=(n-1)2
92÷2=n-1
46=n-1
n=47
middle term is 47+1÷2= 24
24th term will be middle term
= -4+(23)2
= -4+46
=42

Answer 2

The middle term of the arithmetic progression is 42 .

Given:

The arithmetic progression is given: -4 , -2 , 0 ......... 88

To Find:

The middle term of the arithmetic progression

Solution:

The first term(a) of the sequence is -4.

The common difference = $0-(-2)=-2-(-4)=2$

The last term of the Arithmetic progression = 88

We know that the last term of an AP can be calculated using the formula:

$a_n=a+(n-1)d\\\\or, 88 = -4 + (n-1)2\\\\or, 92 = 2n-2\\\\or, 2n = 94\\\\or, n = 47$

Therefore there are 47 terms in the arithmetic sequence.

Now the middle term of the sequence will be at the position of  $\frac{47+1}{2} = 24$ from the beginning of the arithmetic progression.

Therefore the 24th term from the beginning of the arithmetic sequence is

$a_{24}=-4+(24-1)2\\\\or, a_{24}=42$

Hence the middle term of the arithmetic sequence (AP) is 42 .

To learn more about arithmetic sequence (AP)  visit:

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