Math - Sequences and Series

Indicate the first three terms of the following series:

$\sum_{c=3}^{10}(8-5c)$

Explanation

In the arithmetic series, the first terms can be found by plugging in , , and for .

Indicate the first three terms of the following series:

$\sum_{c=3}^{10}(8-5c)$

Explanation

In the arithmetic series, the first terms can be found by plugging in , , and for .

Indicate the first three terms of the following series.

$\sum_{b=2}^{11} \frac{1}{2}(4)^{b-2}$

$\frac{1}{2}+2+8$

$\frac{1}{2}\cdot 2\cdot 8$

$\frac{1}{4}+4+16$

$\frac{1}{4}\cdot 4\cdot 16$

Not enough information

Explanation

The first terms can be found by substituting , , and in for .

$\frac{1}{2}(4)^{2-2}=\frac{1}{2}$

$\frac{1}{2}(4)^{3-2}=2$

$\frac{1}{2}(4)^{4-2}=8$

Indicate the first three terms of the following series.

$\sum_{b=2}^{11} \frac{1}{2}(4)^{b-2}$

$\frac{1}{2}+2+8$

$\frac{1}{2}\cdot 2\cdot 8$

$\frac{1}{4}+4+16$

$\frac{1}{4}\cdot 4\cdot 16$

Not enough information

Explanation

The first terms can be found by substituting , , and in for .

$\frac{1}{2}(4)^{2-2}=\frac{1}{2}$

$\frac{1}{2}(4)^{3-2}=2$

$\frac{1}{2}(4)^{4-2}=8$

Find the sum of all even integers from to .

Explanation

The formula for the sum of an arithmetic series is

$S = \frac{n}{2}(t_{1}+t_{n})$ ,

where is the number of terms in the series, $t_{1}$ is the first term, and $t_{n}$ is the last term.

We know that there are terms in the series. The first term is and the last term is . Our formula becomes:

$S = \frac{50}{2}(250+350)$

Find the sum of all even integers from to .

Explanation

The formula for the sum of an arithmetic series is

$S = \frac{n}{2}(t_{1}+t_{n})$ ,

where is the number of terms in the series, $t_{1}$ is the first term, and $t_{n}$ is the last term.

$S=\frac{30}{2}(2+60)=15(62)=930$

Find the sum of the even integers from to .

Explanation

The sum of even integers represents an arithmetic series.

The formula for the partial sum of an arithmetic series is

$S = \frac{n}{2}(2(a_1)+(n-1)d)$ ,

where is the first value in the series, is the number of terms, and is the difference between sequential terms.

Plugging in our values, we get:

$S = \frac{51}{2}(2(250)+(51-1)2)$

Find the sum of the even integers from to .

Explanation

The sum of even integers represents an arithmetic series.

The formula for the partial sum of an arithmetic series is

$S = \frac{n}{2}(2(a_1)+(n-1)d)$ ,

where is the first value in the series, is the number of terms, and is the difference between sequential terms.

Plugging in our values, we get:

$S = \frac{51}{2}(2(250)+(51-1)2)$

Find the sum of all even integers from to .

Explanation

The formula for the sum of an arithmetic series is

$S = \frac{n}{2}(t_{1}+t_{n})$ ,

where is the number of terms in the series, $t_{1}$ is the first term, and $t_{n}$ is the last term.

We know that there are terms in the series. The first term is and the last term is . Our formula becomes:

$S = \frac{50}{2}(250+350)$

Find the sum of all even integers from to .

Explanation

The formula for the sum of an arithmetic series is

$S = \frac{n}{2}(t_{1}+t_{n})$ ,

where is the number of terms in the series, $t_{1}$ is the first term, and $t_{n}$ is the last term.

$S=\frac{30}{2}(2+60)=15(62)=930$

Sequences and Series

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