Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Write an expression to describe the sequence below. Use $n$ to represent the position of a term in the sequence, where $n = 1$ for the first term. $\newline$ $57, 114, 171, 228, \ldots$ $\newline$ $a_n =$ _____

View step-by-step help

View step-by-step help

Write variable expressions for arithmetic sequences

Full solution

Q. Write an expression to describe the sequence below. Use

n

to represent the position of a term in the sequence, where

n = 1

for the first term.

\newline

57, 114, 171, 228, \ldots

\newline

a_n =

_____

Identify Sequence Type: We have: $\newline$ $57, 114, 171, 228, \ldots$ $\newline$ Is the given sequence geometric or arithmetic? $\newline$ To determine this, we can look at the differences between consecutive terms.
Calculate Differences: Calculate the difference between the second term and the first term: $\newline$ $114 - 57 = 57$ $\newline$ Now, calculate the difference between the third term and the second term: $\newline$ $171 - 114 = 57$ $\newline$ Since the differences are the same, the given sequence is arithmetic.
Find $a_1$ and $d$ : Determine the values of $a_1$ and $d$ of the sequence. $\newline$ The first term, $a_1 = 57$ $\newline$ Common difference, $d = 114 - 57 = 57$
Use nth Term Formula: We have the formula for the nth term of an arithmetic sequence: $\newline$ $a_n = a_1 + (n-1)d$ $\newline$ Substitute the values of $a_1$ and $d$ into the formula: $\newline$ $a_n = 57 + (n-1)\times57$
Simplify Expression: Simplify the expression: $\newline$ $a_{n} = 57 + 57n - 57$ $\newline$ $a_{n} = 57n$

More problems from Write variable expressions for arithmetic sequences

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