Find the missing term in the numeric series: 664, 332, 340, 170, ____, 89, … Identify the number that completes the alternating operation pattern.

Introduction / Context:Many sequences alternate between two simple operations. Here, the values oscillate between halving and adding a constant. We must find the missing value that preserves both alternations.

Given Data / Assumptions:

• Sequence: 664, 332, 340, 170, ?, 89, …
• Exactly one term is missing before 89.

Concept / Approach:Test an alternation: divide by 2, then add a fixed value. Check whether a single constant works.

Step-by-Step Solution:664 ÷ 2 = 332332 + 8 = 340340 ÷ 2 = 170170 + 8 = 178 (this is the missing value)178 ÷ 2 = 89, which matches the next given term

Verification / Alternative check:Continuing the same alternation confirms consistency: after 89, adding 8 would again fit the pattern if extended.

Why Other Options Are Wrong:

• 85 / 97 / 109: None satisfy the required “÷2 then +8” alternation when checked both backward and forward.

Common Pitfalls:Trying a single arithmetic progression. Recognizing alternating ops is key.

Final Answer:178