Question

12, 27, 85, 345, ?

• A. 1737
• B. 1380
• C. 1725
• D. 1731

Hint:

Look for parallel progressions in the multiplier and the addend.

Answer 1

The Correct Option is D

Multiply by \(2,3,4,\ldots\) and then add \(3,4,5,\ldots\): \[ 12\!\times\!2{+}3=27,\quad 27\!\times\!3{+}4=85,\quad 85\!\times\!4{+}5=345. \] Next: \[ 345\!\times\!5{+}6=1725{+}6=1731. \] \[ \boxed{1731} \]

Answer 2

Work backwards from each option using the pattern established by the given terms: after multiplying by \(2,3,4,\ldots\) the constant added also increases by 1 each time (\(3,4,5,\ldots\)), so the step from \(345\) to the missing term should use multiplier \(5\) and addend \(6\). Reverse each option by computing \(\dfrac{\text{option}-6}{5}\) and checking whether it returns \(345\).

1. Option (a) 1737: \(\dfrac{1737-6}{5}=\dfrac{1731}{5}=346.2\), not \(345\) — rejected.
2. Option (b) 1380: \(\dfrac{1380-6}{5}=\dfrac{1374}{5}=274.8\), not \(345\) — rejected.
3. Option (c) 1725: \(\dfrac{1725-6}{5}=\dfrac{1719}{5}=343.8\), not \(345\) — rejected.
4. Option (d) 1731: \(\dfrac{1731-6}{5}=\dfrac{1725}{5}=345\), exactly matching the previous term — confirmed.

Only option (d) reverses cleanly to the known term \(345\), so it is the missing number.

the correct answer is 1731.