Given sequence: 5, ?, 20, 34, 76, 142

To find the missing number in the sequence, we need to identify the pattern or rule that governs the sequence. Let's analyze the given sequence step by step.

1. Difference between consecutive terms:
The difference between the first two terms is unknown. The difference between the second and third terms is 20 - ? = 14. The difference between the third and fourth terms is 34 - 20 = 14. The difference between the fourth and fifth terms is 76 - 34 = 42. The difference between the fifth and sixth terms is 142 - 76 = 66.

From the above differences, we can see that the differences are not constant. So, the sequence does not follow a linear pattern.

2. Squares of the terms:
Let's calculate the square of each term in the sequence:

5^2 = 25
?^2 (unknown term)
20^2 = 400
34^2 = 1156
76^2 = 5776
142^2 = 20164

From the above calculations, we can see that the squares of the terms in the sequence do not follow a consistent pattern. So, the sequence does not follow a quadratic pattern.

3. Alternating pattern of addition and multiplication:
Let's analyze the sequence by alternating between addition and multiplication:

5 + ? = 20
20 * ? = 34
34 + ? = 76
76 * ? = 142

From the above equations, we can solve for the missing number:

5 + ? = 20
? = 20 - 5
? = 15

20 * ? = 34
? = 34 / 20
? = 1.7

34 + ? = 76
? = 76 - 34
? = 42

76 * ? = 142
? = 142 / 76
? ≈ 1.8684

From the analysis, we can see that the missing number in the sequence is 15. The pattern in the sequence is an alternating pattern of addition and multiplication. The missing number is obtained by adding or multiplying the terms in a consistent pattern.