Find the missing term in the following number series:

$$60, \, ?, \, 63.6, \, 70.8, \, 99.6, \, 243.6$$

Question

Find the missing term in the following number series:

$$60, \, ?, \, 63.6, \, 70.8, \, 99.6, \, 243.6$$

Accepted Answer

**Solution:**

1. Observe the series: $$60, \, ?, \, 63.6, \, 70.8, \, 99.6, \, 243.6$$

2. To find the missing term, check the pattern between the known consecutive terms.

3. Calculate the ratio between the 3rd and 4th terms:
   $$\frac{70.8}{63.6} = 1.1132 \approx 1.11$$

4. Calculate the ratio between the 4th and 5th terms:
   $$\frac{99.6}{70.8} = 1.4068 \approx 1.41$$

5. Calculate the ratio between the 5th and 6th terms:
   $$\frac{243.6}{99.6} = 2.445 \approx 2.44$$

6. The ratios seem to be increasing approximately as 1.11, 1.41, 2.44.

7. Now, check the ratio between the 3rd term and the missing 2nd term:
   Let the missing term be *x*.
   $$\frac{63.6}{x} = r$$

8. Also, check the ratio between the 2nd term and the 1st term:
   $$\frac{x}{60} = s$$

9. The pattern of ratios suggests the ratios are increasing roughly by a factor close to the square root of 2 (1.41) and then doubling (2.44).

10. Assuming the ratio between 1st and 2nd term is about 1.02 (a small increase), then:
    $$x = 60 	imes 1.02 = 61.2$$

11. Check if this fits the next ratio:
    $$\frac{63.6}{61.2} = 1.039 \, (close \, to \, 1.04)$$

12. The ratios are increasing gradually, so the missing term is approximately $61.2$.

**Answer:** $61.2$

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