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Algebra 1 : How to find consecutive integers

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Example Question #1 : How To Find Consecutive Integers

The product of two consective positive odd integers is 143. Find both integers.

Possible Answers:

$13\ and\ 15$

$15\ and\ 17$

$11\ and\ 13$

$-11\ and\ -13$

$9\ and\ 11$

Correct answer:

$11\ and\ 13$

Explanation:

If is one odd number, then the next odd number is n+2 . If their product is 143, then the following equation is true.

n(n+2) =143

Distribute into the parenthesis.

n^2+2n=143

Subtract 143 from both sides.

$n^{2} + 2n - 143 = 0$

This can be solved by factoring, or by the quadratic equation. We will use the latter.

$n=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

$n=\frac{-2 \pm \sqrt{4-(4(1)(-143)}}{2} = \frac{-2 \pm \sqrt{576}}{2}=\frac{-2 \pm 24}{2}$

$n=\frac{22}{2}\ or\ n=\frac{-26}{2}$

$n=11\ or\ n=-13$

We are told that both integers are positive, so n=11 .

The other integer is n+2 .

11+2=13

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Example Question #2 : How To Find Consecutive Integers

Write a rule for the following arithmetic sequence:

$\left \{ 2,5,8,11,14,17,20\right \}$

Possible Answers:

x_n=-1+3(n+2)

x_n=-2+3(n-1)

x_n=3+2(n-1)

x_n=2+(n-3)

x_n=2+3(n-1)

Correct answer:

x_n=2+3(n-1)

Explanation:

Know that the general rule for an arithmetic sequence is

x_n=a+d(n-1) ,

where represents the first number in the sequence, is the common difference between consecutive numbers, and is the -th number in the sequence.

In our problem, a=2 .

Each time we move up from one number to the next, the sequence increases by 3. Therefore, d=3 .

The rule for this sequence is therefore x_n=2+3(n-1) .

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Example Question #11 : Other Sequences And Series

If the rule of some particular sequence is written as

x_n=1+3n^2 ,

find the first five terms of this sequence

Possible Answers:

none of these

4,13,28,49,76

4,13,7,9,21

4,17,36,49,33

0,4,13,28,49

Correct answer:

4,13,28,49,76

Explanation:

The first term for the sequence is where n=1 . Thus,

x_1=1+3(1)^2=4

So the first term is 4. Repeat the same thing for the second $\left ( n=2 \right )$ , third $\left ( n=3 \right )$ , fourth $\left ( n=4 \right )$ , and fifth $\left ( n=5 \right )$ terms.

x_2=1+3(2)^2=13

x_3=28

x_4=49

x_5=76

We see that the first five terms in the sequence are

4,13,28,49,76

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Example Question #4 : How To Find Consecutive Integers

What are three consecutive numbers that are equal to ?

Possible Answers:

10, 11, 12

8, 11, 14

1, 11, 21

9, 11, 13

6, 11, 16

Correct answer:

10, 11, 12

Explanation:

When finding consecutive numbers assign the first number a variable.

If the first number is assigned the letter n, then the second number that is consecutive must be n + 1 and the third number must be n + 2 .

Write it out as an equation and it should look like:

n + n + 1 + n + 2 = 33

Simplify the equation then,

3n + 3 = 33

3n = 30

n = 10

If n = 10 then n + 1 = 10 + 1 = 11

And n + 2=10 + 2 = 12

So the answer is 10, 11, 12

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Example Question #5 : How To Find Consecutive Integers

The sum of five odd consecutive numbers add to 935 . What is the fourth largest number?

Possible Answers:

171

189

185

201

191

Correct answer:

185

Explanation:

Let the first number be .

If is an odd number, the next odd numbers will be:

x+2 , x+4 , x+6 , and x+8

The fourth highest number would then be: x+2

Set up an equation where the sum of all these numbers add up to 935 .

x+(x+2)+(x+4)+(x+6)+(x+8) = 935

Simplify this equation.

5x +20= 935

Subtract 20 from both sides.

5x +20-20= 935-20

Simplify both sides.

5x= 915

Divide by five on both sides.

$\frac{5x}{5}= \frac{915}{5}$

x=183

Corresponding to the five numbers, the set of five consecutive numbers that add up to 935 are: [183,185,187,189,191]

The fourth largest number would be 185 .

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Algebra 1 : How to find consecutive integers

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #1 : How To Find Consecutive Integers

Example Question #2 : How To Find Consecutive Integers

Example Question #11 : Other Sequences And Series

Example Question #4 : How To Find Consecutive Integers

Example Question #5 : How To Find Consecutive Integers

All Algebra 1 Resources

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