Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Use the explicit formula to find a recursive formula for the sequence $a$ . Write your answer in simplest form. $\newline$ The recursive formula should depend on $a$ . $\newline$ $a = 3n - 37$ $\newline$ a = ______

View step-by-step help

View step-by-step help

Convert an explicit formula to a recursive formula

Full solution

Q. Use the explicit formula to find a recursive formula for the sequence

a

. Write your answer in simplest form.

\newline

The recursive formula should depend on

a

.

\newline

a = 3n - 37

\newline

a = ______

Identify Sequence Type: Identify if the given sequence is geometric or arithmetic. $\newline$ The explicit formula given is $a = 3n - 37$ , which is a linear function of $n$ and does not involve any exponent terms. Hence, the given sequence is arithmetic.
Find First Term: Find the first term of the sequence using the explicit formula. $\newline$ To find the first term, we substitute $n=1$ into the explicit formula: $\newline$ $a_1 = 3(1) - 37$ $\newline$ $= 3 - 37$ $\newline$ $= -34$
Find Second Term: Find the second term of the sequence using the explicit formula. $\newline$ To find the second term, we substitute $n=2$ into the explicit formula: $\newline$ $a_2 = 3(2) - 37$ $\newline$ $= 6 - 37$ $\newline$ $= -31$
Find Common Difference: Find the common difference in the arithmetic sequence. $\newline$ The common difference, $d$ , is the difference between any two consecutive terms. We can calculate it as follows: $\newline$ $d = a_2 - a_1$ $\newline$ $= -31 - (-34)$ $\newline$ $= -31 + 34$ $\newline$ $= 3$
Write Recursive Formula: Write the recursive formula by plugging in the value of the common difference. $\newline$ We can express the $n$ th term of an arithmetic sequence in terms of the $(n-1)$ th term and the common difference $d$ : $\newline$ $a_n = a_{(n - 1)} + d$ $\newline$ Substituting $3$ for $d$ in the recursive formula, we get: $\newline$ $a_n = a_{(n - 1)} + 3$

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 2 months ago

Question

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

Posted 1 month ago

Question

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

Posted 2 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 2 months ago

Question

What is the missing number in this pattern?

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

Posted 1 month 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 1 month 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 1 month 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 1 month 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 2 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 1 month ago