Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Find the sum of the first 10 terms of the following series, to the nearest integer.

15,30,60,dots
Answer:

Find the sum of the first $10$ terms of the following series, to the nearest integer. $\newline$ $15,30,60, \ldots$ $\newline$ Answer:

View step-by-step help

View step-by-step help

Geometric sequences

Full solution

Q. Find the sum of the first

10

terms of the following series, to the nearest integer.

\newline

15,30,60, \ldots

\newline

Answer:

Identify type of series: Identify the type of series. $\newline$ The given series is geometric because each term is multiplied by a common ratio to get the next term.
Determine common ratio: Determine the common ratio $r$ of the series. $\newline$ To find the common ratio, divide the second term by the first term. $\newline$ $\frac{30}{15} = 2$ $\newline$ Common Ratio $r$ : $2$
Use formula for sum: Use the formula for the sum of the first $n$ terms of a geometric series. $\newline$ The formula for the sum of the first $n$ terms ( $S_n$ ) of a geometric series is: $\newline$ $S_n = a \cdot (1 - r^n) / (1 - r)$ , where $a$ is the first term and $r$ is the common ratio.
Plug values into formula: Plug the values into the formula to find the sum of the first $10$ terms. $a = 15$ (the first term) $r = 2$ (the common ratio) $n = 10$ (the number of terms) $S_{10} = 15 \times (1 - 2^{10}) / (1 - 2)$
Calculate sum: Calculate the sum using the values from Step $4$ . $\newline$ $S_{10} = 15 \times (1 - 1024) / (1 - 2)$ $\newline$ $S_{10} = 15 \times (-1023) / (-1)$ $\newline$ $S_{10} = 15 \times 1023$ $\newline$ $S_{10} = 15345$
Round sum: Round the sum to the nearest integer. The sum is already an integer, so no rounding is necessary.

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