Question

find the middle term of an AP:213,205,197......37

Answer 1

hey mate

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here is ur answer

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Ap = 213,205,197..
...37
a= 213
d= 205-213
8

ap = a+(n-1)d
37= 213+(n-1)8
37-213= (n-1)8
176=(n-1)8
n-1= 176/8
n-1=22
n= 22+1
n=23

middle term
first term + last term / 2

213+37/2
250/2
125

Answer 2

Hii There!!!

Given, A.P = 213, 205, 197 , ...., 37

Here, a = 213 , an = 37 , d = 205 - 213 = (-8) , n= ?

Since, an = a + ( n - 1 ) × d

=> 37 = 213 + ( n - 1 ) × ( - 8 )

=> 213 + ( n - 1 ) × 8 = 37

=> 213 - 37 = 8 ( n - 1 )

=> 176 /8 = ( n - 1 )

=> 22 = ( n - 1 )

=> n = 22 + 1

=> n = 23

Hence, number of terms = 23 terms.

Since ,middle term = ( first term +last term ) / 2

⇒213+37 / 2

⇒250/2

⇒125

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Hope it helps