Question

# Describe the pattern in the numbers 5, -15, 45, -215, ... and write the next three numbers in the pattern.

Hint:

### A pattern is a repeated arrangement of numbers, shapes, colours etc. The Pattern can be related to any type of event or object. If the set of numbers are related to each other in a specific rule, then the rule or manner is called a pattern.

## The correct answer is: Hence, the next three numbers of the sequence will be 645, -1935, 5805 and the pattern here is that every number is (-3) times the previous number.

### Solution

The sequence is given: 5, -15, 45, -215, ...

We can see that

-15 = 5 × -3

45 = -15 × (-3)

-215 = 45 × -3

So we can conclude that the n^{th} number will be the result of multiplication of (n-1)^{th} number with -3 or we can say that every number is (-3) times the previous number.

The next three numbers will be

215× -3 = 645

645 × -3 = -1935

-1935 × -3 = 5805

Final Answer:

Hence, the next three numbers of the sequence will be 645, -1935, 5805 and the pattern here is that every number is (-3) times the previous number.

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### Two rival dry cleaners both advertise their prices. Let x equal the number of items dry cleaned. Store A’s prices are represented by the equation 15x - 2. Store B’s prices are represented by the expression 3 (5x + 7). When do the two stores charge the same rate ? Explain.

Mathematical expressions are made up of at least two numbers or variables, one math operation, and a sentence. This mathematical operation allows you to multiply, divide, add, or subtract numbers.

¶**Types of Expression**

1. Arithmetic operators and numbers make up a mathematical numerical expression. There are no symbols for undefined variables, equality, or inequality.

2. Unknown variables, numerical values, and arithmetic operators make up an algebraic expression. There are no symbols for equality or inequality in it.

¶In contrast to equations, the equal (=) operator is used between two mathematical expressions. Expressions denote a combination of numbers, variables, and operation symbols. The "equal to" sign also has the same value on both sides.