Discussion
The 100th common term between the series 3 + 5 + 7 + 9 + ... and 3 + 6 + 9 + 12 + ... is
Answer: B
The 100th common term is 597.
The first series is the odd numbers from 3, and the second is the multiples of 3. Their common terms are the odd multiples of 3: 3, 9, 15, 21, ..., an arithmetic progression with first term 3 and common difference 6.
\[ \begin{aligned} T_n &= a + (n-1)d \\ T_{100} &= 3 + 99 \times 6 \\ &= 597 \end{aligned} \]
Using \(n\) instead of \(n-1\) gives \(3 + 600 = 603\). 595 and 607 are not odd multiples of 3, and 605 is not a multiple of 3, so none of them can be a common term.
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