Geometric Series

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 found by multiplying the previous term by a fixed, non-zero number called the common ratio.

Front

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

Back

The formula is S_n = a_1 * (1 - r^n) / (1 - r), where S_n is the sum of the first n terms, a_1 is the first term, r is the common ratio, and n is the number of terms.

Front

If a_1 = 4, r = -5, and n = 4, what is the sum of the first n terms?

Back

The sum is -416.

Front

What is the common ratio in the sequence 3, 6, 12, 24, ...?

Back

The common ratio is 2, as each term is multiplied by 2 to get the next term.

Front

Calculate the sum of the first seven terms of the sequence 3, 6, 12, 24, ...

Back

The sum is 381.

Front

What is the common ratio in the sequence 3, 15, 75, 375, ...?

Back

The common ratio is 5.

Front

Calculate the sum of the first three terms of the sequence 3, 15, 75, 375, ...

Back

The sum is 93.

Front

What is the sum of the geometric series: -2 + 6 - 18 + 54 - 162?

Back

The sum is -122.

Front

Define 'geometric series'.

Back

It is the sum of the terms of the geometric sequence.

Front

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

Back

The formula is a_n = a_1 * r^(n-1), where a_n is the nth term, a_1 is the first term, r is the common ratio, and n is the term number.