Discussion

Find the middle term of the A.P. 7, 13, 19, ..., 247.

Answer: C

Correct answer: 127

First count the terms. With \(a = 7\), \(d = 6\) and last term \(l = 247\):

\[247 = 7 + (n-1)6 \quad\Longrightarrow\quad 240 = 6(n-1) \quad\Longrightarrow\quad n = 41\]

With an odd number of terms there is a single middle term, the \(\tfrac{41+1}{2} = 21\)st.

\[a_{21} = 7 + 20 \times 6 = 127\]

As a check, 127 sits exactly halfway between the ends: \(\tfrac{7 + 247}{2} = 127\).

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