We read your photo as:

d) How can what differs be explained in relation to the stage number? e) What rule did you use to complete the table? f) How many matches are needed for figure 9 (or term 9)

Mathematics

ScanSolve AI Answer

Answer

e

Number of matchsticks=3n+1\text{Number of matchsticks} = 3n + 1

Step-by-step solution

4 steps

Here are the solutions for parts d), e), and f):

Part d

How can what differs be explained in relation to the stage number?

The number of squares in each stage is equal to the stage number (nn). The total number of matchsticks increases by 3 for each new stage. This forms an arithmetic sequence where the number of matchsticks is 3n+13n + 1.

Here is the completed table:

Stage12345nAnalysis (Number of squares)12345nTerm Value (Number of matchsticks)471013163n+1\begin{array}{|c|c|c|c|c|c|c|} \hline \text{Stage} & 1 & 2 & 3 & 4 & 5 & n \\ \hline \text{Analysis (Number of squares)} & 1 & 2 & 3 & 4 & 5 & n \\ \hline \text{Term Value (Number of matchsticks)} & 4 & 7 & 10 & 13 & 16 & 3n+1 \\ \hline \end{array}

Part e

Number of matchsticks=3n+1\text{Number of matchsticks} = 3n + 1

What rule did you use to complete the table?

The rule used to complete the table is an arithmetic progression.

  1. Identify the first term and common difference.

    The first term (number of matchsticks for Stage 1) is a1=4a_1 = 4.
    The common difference (increase in matchsticks per stage) is d=3d = 3.

  2. Write the general formula for the nn-th term.

    The formula for the nn-th term of an arithmetic sequence is an=a1+(n−1)da_n = a_1 + (n-1)d.
    Substituting the values:

    an=4+(n−1)3a_n = 4 + (n-1)3 an=4+3n−3a_n = 4 + 3n - 3 an=3n+1a_n = 3n + 1

    The rule is Number of matchsticks=3n+1\boxed{\text{Number of matchsticks} = 3n + 1}.

Part f· 2 steps

How many matches are needed for figure 9 (or term 9)?

  1. Use the rule derived in part e).

    The rule is an=3n+1a_n = 3n + 1.

  2. Substitute n=9n=9 into the rule.

    a9=3(9)+1a_9 = 3(9) + 1 a9=27+1a_9 = 27 + 1 a9=28a_9 = 28

    For figure 9, 28 matches are needed.

Was this helpful?

Try one yourself

A new problem that tests the same skill.

Still stuck on this one?

Ask a follow-up, and the answer starts from this question.

Got a different question?Ask your own question

More Mathematics Questions

QLook at the pattern below. a) What shape are the matches arranged in? b) Describe the pattern rule…QA pattern is made using matchsticks. b) Complete the table. c) Write down the rule in your own…QUse TABLE 1 above and match a definition with the terminology below. Write only the letter (A-I)…QComplete the table and find the general rule for the pattern: 3; 5; 7; 9...QStudy the pattern below and answer the question that follows. Draw a table to represent stage 1 to…
See all Mathematics questions →
Got a syllabus? Photograph it and I'll tell you what's due and what's worth the most.