Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Find the first five terms of the sequence defined below, where $n$ represents the position of a term in the sequence. Start with $n = 1$ . $\newline$ $2(4)^n$ $\newline$ ___, _, _, _, ___

View step-by-step help

View step-by-step help

Evaluate variable expressions for Sequences

Full solution

Q. Find the first five terms of the sequence defined below, where

n

represents the position of a term in the sequence. Start with

n = 1

.

\newline

2(4)^n

\newline

_____, _____, _____, _____, _____

Find First Term: To find the first term when $n=1$ , plug in $n=1$ into the formula $2(4)^n$ . $\newline$ Calculation: $2(4)^1 = 2 \times 4 = 8$ .
Calculate Second Term: For the second term when $n=2$ , plug in $n=2$ into the formula $2(4)^n$ . $\newline$ Calculation: $2(4)^2 = 2 \times 16 = 32$ .
Determine Third Term: Now, find the third term with $n=3$ , using the same formula $2(4)^n$ . $\newline$ Calculation: $2(4)^3 = 2 \times 64 = 128$ .
Compute Fourth Term: For the fourth term, $n=4$ , so we do the same thing, $2(4)^n$ . Calculation: $2(4)^4 = 2 \times 256 = 512$ .
Find Fifth Term: Finally, for the fifth term, $n=5$ , we use the formula again, $2(4)^n$ . $\newline$ Calculation: $2(4)^5 = 2 \times 1024 = 2048$ .

More problems from Evaluate variable expressions for Sequences

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