Let's break down the questions and solve them one by one:

Question 17:

The sequence given is $10, 11, 11, 12, 13, 13, 14, \dots$. The pattern alternates between repeating a number and increasing by 1 after the repetition. Let's observe the pattern:

• 10 appears once, 11 appears twice, 12 appears once, 13 appears twice, 14 appears once, and so on.

So the sequence looks like this: $10, 11, 11, 12, 13, 13, 14, \dots$

To find the nth term of the sequence, notice that for every even position, we have a repeated number, and for every odd position, we have a unique increasing number. Therefore, we can express the sequence based on this alternating pattern.

Formula for the nth term:

• If n is odd: The term is $5 + \left(\frac{n + 1}{2}\right)$
• If n is even: The term is $5 + \left(\frac{n}{2}\right)$

Question 18:

This describes a pile of stones with 10 layers. The bottom layer has 32 stones, and each layer above has fewer stones. Specifically:

• The first layer has 32 stones.
• The second layer has 30 stones.
• The third layer has 28 stones, and so on.

So, the sequence of stones per layer follows the pattern: 32, 30, 28, ...

This is an arithmetic sequence where the first term is $a_1 = 32$ and the common difference $d = -2$ (since each layer has 2 fewer stones than the one below it).

Formula for the nth term of the sequence:

The formula for the nth term of an arithmetic sequence is: $a_n = a_1 + (n-1) \cdot d$

In this case: $a_n = 32 + (n-1) \cdot (-2)$ $a_n = 32 - 2(n-1)$ $a_n = 32 - 2n + 2$ $a_n = 34 - 2n$

For example:

• The 1st term: $a_1 = 34 - 2(1) = 32$
• The 2nd term: $a_2 = 34 - 2(2) = 30$
• The 3rd term: $a_3 = 34 - 2(3) = 28$ And so on.

Would you like further details on these sequences or additional steps?