Find the missing term :17, 23, 35, 53, 77, ?, 143Question 10Answera.104b.105c.107d.106

1. Break Down the Problem

We have a sequence of numbers: 17, 23, 35, 53, 77, ?, 143. We need to find the missing term that follows this pattern.

2. Relevant Concepts

To identify the pattern, we will look at the differences between consecutive terms in the sequence.

3. Analysis and Detail

Let's calculate the differences between the terms:

• Between 17 and 23:
  $23 - 17 = 6$

• Between 23 and 35:
  $35 - 23 = 12$

• Between 35 and 53:
  $53 - 35 = 18$

• Between 53 and 77:
  $77 - 53 = 24$

Now, we have a list of differences:
6, 12, 18, 24.

Now let's find the differences of these differences:

• Between 6 and 12:
  $12 - 6 = 6$

• Between 12 and 18:
  $18 - 12 = 6$

• Between 18 and 24:
  $24 - 18 = 6$

We see that the second differences are constant at 6. This indicates a quadratic relationship.

To predict the next term in the difference sequence (after 24), we can add 6:
$24 + 6 = 30$

Now, add this to the last known term in the original sequence (77):
$77 + 30 = 107$

4. Verify and Summarize

To verify, let's calculate the next term in the original sequence:
The sequence with the missing term included would be:

• 17, 23, 35, 53, 77, 107

Now, let's check the difference from 107 to the next known term 143:
$143 - 107 = 36$
This continues the pattern, as the differences are now 6, 12, 18, 24, 30, 36.

Final Answer

The missing term is 107, therefore, the correct answer is:
c. 107.