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Question
Find the middle term of the A.P. 6, 13, 20, ... , 216.
Solution
The given arithmetic progression is 6, 13, 20, ..., 216
Let 216 be the nth term of the given AP.
So,
a = 6
d = 7
an = 216
Now,
an=a+(n−1)d
⇒216=6+(n−1)×7
⇒7(n−1)=210
⇒n−1 = `210/7`= 30
⇒n=31, which is odd
∴ Middle term of the AP
`=((31+1)/2)th` term of the AP
= 16th term of the AP
∴a16=6+(16−1)×7=6+15×7=6+105=111
Thus, the middle term of the given AP is 111.
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