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Find the middle term of the A.P. 6, 13, 20, ... , 216. - Mathematics

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Find the middle term of the A.P. 6, 13, 20, ... , 216.

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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+(n1)d

216=6+(n1)×7

7(n1)=210

n1 = `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+(161)×7=6+15×7=6+105=111

Thus, the middle term of the given AP is 111.

Concept: Arithmetic Progression
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