Arithmetic 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.

Front

What is the common difference in an arithmetic sequence?

Back

The common difference is the fixed amount added to each term to get the next term in the sequence.

Front

Is the sequence 3, 15, 75 an arithmetic sequence?

Back

No, it is not an arithmetic sequence because the differences between terms are not constant.

Front

Is the sequence 24, 15, 6 an arithmetic sequence?

Back

Yes, it is an arithmetic sequence with a common difference of -9.

Front

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

Back

The nth term 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

Find the 63rd term of the arithmetic sequence -1, 5, 11.

Back

The 63rd term is 371.

Front

Which of the following is an arithmetic sequence: 5, 12, 21, 32, 45 or 3, 6, 12, 24, 48?

Back

5, 12, 21, 32, 45 is an arithmetic sequence with a common difference of 7.

Front

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

Back

The sum S_n of the first n terms is given by S_n = n/2 * (a_1 + a_n), where a_n is the nth term.

Front

Find the 75th term of the arithmetic sequence -17, -13, 9.

Back

The 75th term is 279.

Front

What is the first term of the arithmetic sequence 2, 5, 8, ...?

Back

The first term is 2.