Arithmetic-Geometric series

Front

What is an Arithmetic-Geometric series?

Back

An Arithmetic-Geometric series is a series where each term is the product of an arithmetic sequence and a geometric sequence.

Front

Define the common ratio in a geometric series.

Back

The common ratio (r) in a geometric series is the factor by which each term is multiplied to obtain the next term.

Front

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

Back

Front

How do you find the nth term of a geometric series?

Back

Front

What is the first term in the series 1, 5, 25, 125?

Back

The first term (a) is 1.

Front

If the common ratio of a geometric series is 5, what is the second term if the first term is 1?

Back

The second term is 1 x 5 = 5.

Front

What happens to the sum of a geometric series if the common ratio is greater than 1?

Back

If the common ratio is greater than 1, the sum diverges to infinity as n approaches infinity.

Front

Can the sum of a geometric series be negative?

Back

Yes, if the first term is negative and the common ratio is positive but less than 1, the sum can be negative.

Front

What is the significance of the common ratio being less than 1 in a geometric series?

Back

If the common ratio is less than 1, the series converges, meaning the sum approaches a finite limit as n increases.

Front

What is the sum of the first 4 terms of the geometric series 1 + 0.5 + 0.25 + ?

Back

The sum is 1.875.