Given the number series:

$$A, \quad 29, \quad B, \quad C, \quad 437, \quad B + 687, \quad \frac{1294}{A}$$

where *n* is a positive integer and the difference between 29 and *B* is *X*. The number *X* has exactly 3 factors excluding itself, which are 13, 5, and *A*. Including *X*, the total number of factors becomes 4.

What is the value of $A + C$?

Question

Given the number series:

$$A, \quad 29, \quad B, \quad C, \quad 437, \quad B + 687, \quad \frac{1294}{A}$$

where *n* is a positive integer and the difference between 29 and *B* is *X*. The number *X* has exactly 3 factors excluding itself, which are 13, 5, and *A*. Including *X*, the total number of factors becomes 4.

What is the value of $A + C$?

Accepted Answer

**Solution:**

1. Let the difference between 29 and *B* be *X*.

2. Given that *X* has exactly 3 factors excluding itself: 13, 5, and *A*. Including *X*, total factors are 4.

3. Since 13 and 5 are factors of *X*, *X* must be their product: $13 	imes 5 = 65$.

4. The factors of 65 are 1, 5, 13, and 65. Here, *A* is 1 (the missing factor from the given list).

5. Therefore, $X = 65$ and $B = 29 + 65 = 94$.

6. The series given is:

$$A = 1, \quad 29, \quad 94, \quad C, \quad 437, \quad 781, \quad 1294$$

7. To find *C*, observe the pattern in the series. The difference between terms seems to increase by 60 each time:

- $29 - 1 = 28$
   - $94 - 29 = 65$
   - $C - 94 = ?$

But from the original solution, $C = 94 + 125 + 1 = 220$ (where 125 is an increment pattern).

8. So, $C = 220$.

9. Finally, calculate $A + C = 1 + 220 = 221$.

**Answer:** $221$

Answer

Answer

Answer