Question

daily word problems wednesday-week 8 maria is proud of her seashell collection. she has 9 boxes of seashells. the first box has 1 seashell in it. the second has 2 seashells in it, the third has 3, and so on. how many seashells does maria have in all 9 boxes? name: work space: answer: ______ seashells in all

Explanation:

Step1: Identify the sequence type

The number of seashells in each box forms an arithmetic sequence where the first term \(a_1 = 1\), the common difference \(d = 1\), and the number of terms \(n = 9\).

Step2: Use the sum formula for an arithmetic sequence

The sum \(S_n\) of the first \(n\) terms of an arithmetic sequence is given by the formula \(S_n=\frac{n(a_1 + a_n)}{2}\), where \(a_n\) is the \(n\)-th term. First, we find the 9th term \(a_9\). For an arithmetic sequence, \(a_n=a_1+(n - 1)d\). Substituting \(a_1 = 1\), \(n = 9\), and \(d = 1\), we get \(a_9=1+(9 - 1)\times1=1 + 8=9\).

Step3: Calculate the sum

Now, we use the sum formula \(S_9=\frac{9\times(1 + 9)}{2}\). First, calculate the sum inside the parentheses: \(1+9 = 10\). Then, multiply by 9: \(9\times10 = 90\). Finally, divide by 2: \(\frac{90}{2}=45\).

Answer:

45