Chapter 11: Q50. (page 582)

Refer to the first three arrays of numbers below.
Write an equation representing the nth number in this pattern?

Short Answer

Expert verified

The equation representing the nth number in the pattern is $4 n - 3$ .

Step by step solution

Step 1. Given Information.

Given pattern is:

Step 2. Calculation.

The n^th term of an arithmetic sequence is given by $a_{n} = a_{1} + (n - 1) d$ .

Here the first term is $a_{1} = 1$

The difference between the first two terms is $5 - 1 = 4$

The difference between the next two terms is $9 - 5 = 4$

Hence, the common difference is $d = 4$

Plugging the values in the formula:

$\begin{array}{l} a_{n} = a_{1} + (n - 1) d \\ a_{n} = 1 + (n - 1) (4) \\ a_{n} = 1 + 4 n - 4 \\ a_{n} = 4 n - 3 \end{array}$

Step 3. Conclusion.

Hence, the equation representing the nth number in the pattern is $4 n - 3$

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Refer to the first three arrays of numbers below.
Write an equation representing the nth number in this pattern?

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Calculation.

Step 3. Conclusion.

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Refer to the first three arrays of numbers below.Write an equation representing the nth number in this pattern?

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Calculation.

Step 3. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Calculus

Logic and Functions

Theoretical and Mathematical Physics

Applied Mathematics

Statistics

Study anywhere. Anytime. Across all devices.

Refer to the first three arrays of numbers below.
Write an equation representing the nth number in this pattern?