Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Write an explicit formula that represents the sequence defined by the following recursive formula:

a_(1)=8" and "a_(n)=a_(n-1)-2
Answer:
a_(n)=

Write an explicit formula that represents the sequence defined by the following recursive formula: $\newline$ $a_{1}=8 \text { and } a_{n}=a_{n-1}-2$ $\newline$ Answer: $a_{n}=$

View step-by-step help

View step-by-step help

Convert an explicit formula to a recursive formula

Full solution

Q. Write an explicit formula that represents the sequence defined by the following recursive formula:

\newline

a_{1}=8 \text { and } a_{n}=a_{n-1}-2

\newline

Answer:

a_{n}=

Identify Pattern: To find the explicit formula for the given recursive sequence, we need to determine a pattern that relates the term number $n$ directly to its value without relying on the previous term.
Write Out Terms: Let's start by writing out the first few terms of the sequence using the recursive formula: $\newline$ $a_{1} = 8$ (given) $\newline$ $a_{2} = a_{1} - 2 = 8 - 2 = 6$ $\newline$ $a_{3} = a_{2} - 2 = 6 - 2 = 4$ $\newline$ $a_{4} = a_{3} - 2 = 4 - 2 = 2$ $\newline$ From this pattern, we can see that each term is $2$ less than the previous term.
Determine Relationship: Now, let's find the relationship between the term number $n$ and the term value. We can see that: $\newline$ $a_{1} = 8 = 8 - 2(1 - 1)$ $\newline$ $a_{2} = 6 = 8 - 2(2 - 1)$ $\newline$ $a_{3} = 4 = 8 - 2(3 - 1)$ $\newline$ $a_{4} = 2 = 8 - 2(4 - 1)$ $\newline$ It seems that the term value is equal to $8$ minus $2$ times $(n - 1)$ .
Generalize Formula: To confirm the pattern, let's generalize the formula: $\newline$ $a_{n} = 8 - 2(n - 1)$ $\newline$ Simplifying the formula, we get: $\newline$ $a_{n} = 8 - 2n + 2$ $\newline$ $a_{n} = 10 - 2n$ $\newline$ This is the explicit formula for the given sequence.

More problems from Convert an explicit formula to a recursive formula

Question

Find the sum of the finite arithmetic series.

\sum_{n=1}^{10} (7n+4)

\newline

Posted 9 months ago

Question

Type the missing number in this sequence: `55,\59,\63,\text{_____},\71,\75,\79`

Posted 5 months ago

Question

Type the missing number in this sequence: `2, 4 8`, ______,`32`

Posted 5 months ago

Question

What kind of sequence is this?

2, 10, 50, 250, \ldots

Choices:Choices:

\newline

\text{[A]arithmetic}

\newline

\text{[B]geometric}

\newline

\text{[C]both}

\newline

\text{[D]neither}

Posted 5 months ago

Question

What is the missing number in this pattern?

1, 4, 9, 16, 25, 36, 49, 64, 81, \_\_\_\_

Posted 7 months ago

Question

Classify the series.

\sum_{n = 0}^{12} (n + 2)^3

\newline

\newline

\text{[A]arithmetic}

\newline

\text{[B]geometric}

\newline

\text{[C]both}

\newline

\text{[D]neither}

Posted 5 months ago

Question

Find the first three partial sums of the series.

\newline

1 + 6 + 11 + 16 + 21 + 26 + \cdots

\newline

Write your answers as integers or fractions in simplest form.

\newline

S_1 =

\newline

S_2 =

\newline

S_3 =

Posted 7 months ago

Question

Find the third partial sum of the series.

\newline

3 + 9 + 15 + 21 + 27 + 33 + \cdots

\newline

Write your answer as an integer or a fraction in simplest form.

\newline

S_3 =

Posted 7 months ago

Question

Find the first three partial sums of the series.

\newline

1 + 7 + 13 + 19 + 25 + 31 + \cdots

\newline

Write your answers as integers or fractions in simplest form.

\newline

S_1 =

\newline

S_2 =

\newline

S_3 =

Posted 9 months ago

Question

Does the infinite geometric series converge or diverge?

\newline

1 + \frac{3}{4} + \frac{9}{16} + \frac{27}{64} + \cdots

\newline

\newline

\text{[A]converge}

\newline

\text{[B]diverge}

Posted 5 months ago

Related topics

Algebra - Order of Operations Algebra - Distributive Property `X` and `Y` Axes Geometry - Scalene Triangle Common Multiple Geometry - Quadrant