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

Step 1: Divide each term by the one before it: \(27/12=2.25,\ 85/27\approx3.15,\ 345/85\approx4.06\); the ratios drift toward \(2,3,4\), so the next ratio should be near \(5\).

Step 2: Estimate the next term using that ratio: \(345\times5=1725\).

Step 3: The small excess in each ratio comes from an add-on that grows by \(1\) every step (\(+3,+4,+5,\ldots\)), so the next add-on is \(+6\): \(1725+6=1731\).
\[ \boxed{1731} \]