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Question

Find the middle term of the AP $$6,13, 20 ,........,216$$.


Solution

Given,
$$a=6$$

$$d=13-6=7$$

$$T_n=a+(n-1)d$$

$$216=6+(n-1)7$$

$$\therefore n=31$$

If $$n$$ is odd then the middle term is $$\dfrac {n+1}{2}$$ 

Middle term, $$=\dfrac{31+1}{2}=16$$

$$T_{16}=6+(16-1)7=111$$.

Mathematics

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