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Number and Algebra

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What is scientific notation?

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A way to express numbers as a product of a coefficient (between 1 and 10) and a power of 10.

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What is scientific notation?

A way to express numbers as a product of a coefficient (between 1 and 10) and a power of 10.

How is the number 3,500,000 expressed in scientific notation?

$3.5 \times 10^6$.

How is the number 0.00000072 expressed in scientific notation?

$7.2 \times 10^{-7}$.

What is an arithmetic sequence?

A sequence with a constant difference between consecutive terms.

What is the formula for the nth term of an arithmetic sequence?

$a_n = a_1 + (n-1)d$.

What do $a_1$ and $d$ represent in the arithmetic sequence formula?

$a_1$ is the first term, and $d$ is the common difference.

What is a geometric sequence?

A sequence with a constant ratio between consecutive terms.

What is the formula for the nth term of a geometric sequence?

$a_n = a_1 \times r^{n-1}$.

What do $a_1$ and $r$ represent in the geometric sequence formula?

$a_1$ is the first term, and $r$ is the common ratio.

What is a series in mathematics?

The sum of the terms in a sequence.

What is the formula for the sum of the first n terms of an arithmetic series?

$S_n = \frac{n}{2}(a_1 + a_n)$.

What is the formula for the sum of the first n terms of a geometric series when $r \neq 1$?

$S_n = \frac{a_1(1-r^n)}{1-r}$.

What is the significance of scientific notation?

It allows for efficient representation of very large or very small numbers.

What is the common difference in an arithmetic sequence?

The constant amount added to each term to get the next term.

What is the common ratio in a geometric sequence?

The constant factor multiplied to each term to get the next term.

How can you identify an arithmetic sequence?

By checking if the difference between consecutive terms is constant.

How can you identify a geometric sequence?

By checking if the ratio between consecutive terms is constant.

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1 / 17

What is scientific notation?

Flip

Spacebar

A way to express numbers as a product of a coefficient (between 1 and 10) and a power of 10.

Flip

Spacebar

What is scientific notation?

A way to express numbers as a product of a coefficient (between 1 and 10) and a power of 10.

How is the number 3,500,000 expressed in scientific notation?

$3.5 \times 10^6$.

How is the number 0.00000072 expressed in scientific notation?

$7.2 \times 10^{-7}$.

What is an arithmetic sequence?

A sequence with a constant difference between consecutive terms.

What is the formula for the nth term of an arithmetic sequence?

$a_n = a_1 + (n-1)d$.

What do $a_1$ and $d$ represent in the arithmetic sequence formula?

$a_1$ is the first term, and $d$ is the common difference.

What is a geometric sequence?

A sequence with a constant ratio between consecutive terms.

What is the formula for the nth term of a geometric sequence?

$a_n = a_1 \times r^{n-1}$.

What do $a_1$ and $r$ represent in the geometric sequence formula?

$a_1$ is the first term, and $r$ is the common ratio.

What is a series in mathematics?

The sum of the terms in a sequence.

What is the formula for the sum of the first n terms of an arithmetic series?

$S_n = \frac{n}{2}(a_1 + a_n)$.

What is the formula for the sum of the first n terms of a geometric series when $r \neq 1$?

$S_n = \frac{a_1(1-r^n)}{1-r}$.

What is the significance of scientific notation?

It allows for efficient representation of very large or very small numbers.

What is the common difference in an arithmetic sequence?

The constant amount added to each term to get the next term.

What is the common ratio in a geometric sequence?

The constant factor multiplied to each term to get the next term.

How can you identify an arithmetic sequence?

By checking if the difference between consecutive terms is constant.

How can you identify a geometric sequence?

By checking if the ratio between consecutive terms is constant.