Front

What is an arithmetic series?

Back

An arithmetic series is the sum of the terms of an arithmetic sequence, where each term after the first is obtained by adding a constant difference to the previous term.

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

Back

The formula is: S_n = \frac{n}{2} (a + l), where S_n is the sum of the first n terms, a is the first term, l is the last term, and n is the number of terms.

Front

What is a geometric series?

Back

A geometric series is the sum of the terms of a geometric sequence, where each term after the first is obtained by multiplying the previous term by a constant ratio.

Tags

CCSS.HSA.SSE.B.4

Front

What is the formula for the sum of the first n terms of a geometric series?

Back

The formula is: S_n = a \frac{(1 - r^n)}{(1 - r)}, where S_n is the sum of the first n terms, a is the first term, r is the common ratio, and n is the number of terms.

Tags

CCSS.HSA.SSE.B.4

Front

How do you find the total earnings of an employee with a fixed raise each year?

Back

Use the formula for the sum of an arithmetic series: S_n = \frac{n}{2} (2a + (n-1)d), where a is the initial salary, d is the raise, and n is the number of years.

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Calculate the total earnings over 5 years for a salary of $48,000 with a $1,340 raise each year.

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Total earnings = $48,000 + $49,340 + $50,680 + $52,020 + $53,360 = $253,400.

Tags

CCSS.HSF.BF.A.2

Front

What is the common difference in an arithmetic series?

Back

The common difference is the constant amount added to each term to get the next term in the series.

Tags

CCSS.HSF.BF.A.2

Front

How do you find the sum of the first n even numbers?

Back

The sum of the first n even numbers can be calculated using the formula: S_n = n(n + 1).

Front

What is the common ratio in a geometric series?

Back

The common ratio is the factor by which each term in the series is multiplied to obtain the next term.

Tags

CCSS.HSF.BF.A.2

Front

Calculate the sum of the first 718 terms of the series 2 + 4 + 6 + ... + 1436.

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The sum is 516,242.