Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Find the sum of the first 6 terms of the following series, to the nearest integer.

20,10,5,dots
Answer:

Find the sum of the first $6$ terms of the following series, to the nearest integer. $\newline$ $20,10,5, \ldots$ $\newline$ Answer:

View step-by-step help

View step-by-step help

Geometric sequences

Full solution

Q. Find the sum of the first

6

terms of the following series, to the nearest integer.

\newline

20,10,5, \ldots

\newline

Answer:

Identify type and ratio: Identify the type of series and the common ratio. $\newline$ The given series is geometric because each term is obtained by multiplying the previous term by a constant ratio. $\newline$ To find the common ratio $r$ , we divide the second term by the first term. $\newline$ $r = \frac{10}{20} = 0.5$
Use formula for sum: Use the formula for the sum of the first $n$ terms of a geometric series. $\newline$ The sum $S_n$ of the first $n$ terms of a geometric series is given by the formula: $\newline$ $S_n = a \times (1 - r^n) / (1 - r)$ , where $a$ is the first term, $r$ is the common ratio, and $n$ is the number of terms. $\newline$ In this case, $a = 20$ , $r = 0.5$ , and $n = 6$ .
Calculate sum of terms: Calculate the sum of the first $6$ terms. $\newline$ $S_6 = 20 \times (1 - 0.5^6) / (1 - 0.5)$ $\newline$ $S_6 = 20 \times (1 - 0.015625) / 0.5$ $\newline$ $S_6 = 20 \times 0.984375 / 0.5$ $\newline$ $S_6 = 19.6875 / 0.5$ $\newline$ $S_6 = 39.375$ $\newline$ Since we need to round to the nearest integer, the sum is approximately $39$ .

More problems from Geometric 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