Determine the pattern rule for the given sequence of matchsticks.

May 17, 2026Mathematics

ScanSolve AI Answer

May 17, 2026

Answer

2n + c$.

2.4. Step 1: Determine the pattern rule. The differences in the number of matchsticks for corresponding differences in pattern numbers are constant. For example, from $n=1$ to $n=2$ , $\Delta n = 1$ and $\Delta M = 5-3=2$ . From $n=2$ to $n=4$ , $\Delta n = 2$ and $\Delta M = 9-5=4$ . The ratio $\frac{\Delta M}{\Delta n} = \frac{2}{1} = \frac{4}{2} = 2$ . This indicates a linear relationship of the form $M = 2n + c$ . Using the point $(1, 3)$ from the table:

Was this helpful?

Need help with your own homework?

Get instant step-by-step solutions to any question. Free to start.

Ask Your Question

Handwritten Step-by-Step Solution

Get this as a handwritten image on WhatsApp — like a tutor wrote it for you.

Try on WhatsApp

More Mathematics Questions

Qएक स्कूल के अनुपस्थित छात्रों की संख्या प्रतिदिन 147 दिनों तक दर्ज की गई थी तथा प्राप्त आँकड़े निम्न…QIf y = sinh(ksin⁻¹x), show that (1-x²)y'' - xy' - k²y = 0 Qनिम्नलिखित संचयी बारम्बारता बंंटन से विद्यार्थियों के अंकों का समान्तर माध्य ज्ञात कीजिए—Qनिम्नलिखित बारम्बारता सारणी में छात्रों के प्राप्तांकों का समान्तर माध्य 30 है, अज्ञात बारम्बारताएँ…Qनिम्न आँकड़ों का समान्तर माध्य पद-विच्छलन विधि द्वारा ज्ञात कीजिए—

See all Mathematics questions →

Still have questions?

Quick Answer

2.4. Step 1: Determine the pattern rule.

Asked on May 17, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on May 17, 2026

2.4. Step 1: Determine the pattern rule. The differences in the number of matchsticks for corresponding differences in pattern numbers are constant. For example, from n=1 to n=2, n = 1 and M = 5-3=2. From n=2 to n=4, n = 2 and M = 9-5=4. The ratio ( M)/( n) = (2)/(1) = (4)/(2) = 2. This indicates a linear relationship of the form M = 2n + c. Using the point (1, 3) from the table: