Given the series II: $100, W, X, Y, Z, 32$ where the terms follow the same pattern as Series I: $60, 120, 24, 48, 9.6, 19.2$ which follows the pattern $ imes 2, \div 5, imes 2, \div 5, \ldots$, and knowing that $W = 200$, $X = 40$, $Y = 80$, and $Z = 16$, if a new series starts with the value $(W - X)$ and follows the same logic, what is the 3rd term of this newly formed series?

Question

Given the series II: $100, W, X, Y, Z, 32$ where the terms follow the same pattern as Series I: $60, 120, 24, 48, 9.6, 19.2$ which follows the pattern $	imes 2, \div 5, 	imes 2, \div 5, \ldots$, and knowing that $W = 200$, $X = 40$, $Y = 80$, and $Z = 16$, if a new series starts with the value $(W - X)$ and follows the same logic, what is the 3rd term of this newly formed series?

Accepted Answer

**Solution:**

1. The given Series I is: $60, 120, 24, 48, 9.6, 19.2$.
   - The pattern alternates between multiplying by 2 and dividing by 5.
   - Specifically: $	imes 2, \div 5, 	imes 2, \div 5, 	imes 2, \ldots$

2. Series II is: $100, W, X, Y, Z, 32$ with $W=200$, $X=40$, $Y=80$, $Z=16$.
   - This series follows the same pattern:
     - $100 	imes 2 = 200 = W$
     - $200 \div 5 = 40 = X$
     - $40 	imes 2 = 80 = Y$
     - $80 \div 5 = 16 = Z$
     - $16 	imes 2 = 32$

3. The new series starts with the value $(W - X) = 200 - 40 = 160$.

4. Applying the same pattern starting from $160$:
   - 1st term: $160$
   - 2nd term: $160 	imes 2 = 320$
   - 3rd term: $320 \div 5 = 64$
   - 4th term: $64 	imes 2 = 128$
   - 5th term: $128 \div 5 = 25.6$

5. However, the question asks for the 3rd term of the newly formed series.
   - The 3rd term is $64$.

**But notice the options and the pattern:**
- The options include $64$ and $144$.

6. Re-examining the question, it states "following the same logic mentioned in the above series".
   - The original series alternates $	imes 2$ and $\div 5$.
   - The new series starts at $(W - X) = 160$.

7. Let's verify the 3rd term again:
   - 1st term: $160$
   - 2nd term: $160 	imes 2 = 320$
   - 3rd term: $320 \div 5 = 64$

8. Therefore, the 3rd term is $64$.

**Answer:** $64$

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