Find the middle term of the A.P. 213, 205, 197, ..., 37. If the 3rd
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- Let a be the first term and d be the common difference ...
We know that , nth term = an = a + ( n − 1 ) d
dIt is given that a = 213 , d = −8 and an = 37
, d = −8 and an = 37According to the question ..,
⇒ 37 = 213 + (n − 1)(−8)
⇒ 37 = 213 − 8n + 8
⇒ 8n = 221 − 37
⇒ 8n = 184
⇒ n = 23 .... (1)
Therefore, total number of terms is 23 ...
.Since , there are odd number of terms ...
.So , Middle term will be ( 23 + 1 / 2 )th
Term , i.e., the 12th term ...
.∴ A¹² = 213 + ( 12 − 1 )( −8 )
= 213 − 88
= 125
Thus , the middle term of the A.P. 213 , 205 , 197 , ...., 37 is 125 ...
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