Arithmetic and Geometric Sequences

Front

What is an arithmetic sequence?

Back

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

Front

What is a geometric sequence?

Back

A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.

Front

How do you find the nth term of an arithmetic sequence?

Back

The nth term of an arithmetic sequence can be found using the formula: \( a_n = a_1 + (n-1)d \), where \( a_1 \) is the first term and \( d \) is the common difference.

Front

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

Back

The nth term of a geometric sequence can be found using the formula: \( a_n = a_1 \cdot r^{(n-1)} \), where \( a_1 \) is the first term and \( r \) is the common ratio.

Front

What is the common difference in the sequence 2, 5, 8, 11, ...?

Back

The common difference is 3, as each term increases by 3.

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

Find the 8th term of the sequence 3, 6, 12, 24, ...

Back

The 8th term is 384.

Front

Identify the type of sequence: 135, 45, 15, 5, ...

Back

This is a geometric sequence with a common ratio of \( \frac{1}{3} \).

Front

What is the formula for the sequence with first three terms 3, 11, 19?

Back

The formula is \( a_n = 3 + 8(n-1) \).

Front

Calculate a_5 for the sequence defined by \( a_n = 5 \cdot 2^{(n-1)} \).

Back

a_5 = 80.