Arithmetic Sequences and Formulas

Front

What is an arithmetic sequence?

Back

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant.

Front

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

Back

The nth term of an arithmetic sequence can be expressed as aₙ = a₁ + (n - 1)d, where a₁ is the first term and d is the common difference.

Front

How do you find the first six terms of the sequence defined by aₙ = n³ - n²?

Back

Substitute n = 1, 2, 3, 4, 5, 6 into the formula to get the terms: 0, 4, 18, 48, 100, 180.

Front

What is the significance of the slope in a linear equation?

Back

The slope indicates the steepness and direction of the line; it is the ratio of the change in y to the change in x.

Front

What does it mean if the slope is undefined?

Back

An undefined slope occurs when a line is vertical, meaning there is no change in x while y changes.

Front

How do you determine the equation of a line given two points?

Back

Use the slope formula to find the slope, then apply the point-slope form of the equation: y - y₁ = m(x - x₁).

Front

What is the formula for the nth term of the sequence defined by aₙ = (n + 4)/(n + 2)?

Back

To find the nth term, substitute n into the formula: aₙ = (n + 4)/(n + 2).

Front

How do you find the first six terms of the sequence defined by aₙ = (n + 4)/(n + 2)?

Back

Substitute n = 1, 2, 3, 4, 5, 6 into the formula to get the terms: 5/3, 3/2, 7/5, 4/3, 9/7, 5/4.

Front

What is the formula for the number of bricks in a stacked pile where each row has three fewer bricks than the row below?

Back

The formula is aₙ = 42 - 3(n - 1), where 42 is the number of bricks in the bottom row.

Front

How do you find the number of bricks in the 7th row using the formula aₙ = 42 - 3(n - 1)?

Back

Substitute n = 7 into the formula: a₇ = 42 - 3(7 - 1) = 24.