Arithmetic Sequences1

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 the formula for the nth term of an arithmetic sequence?

Back

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

Front

If the first term of an arithmetic sequence is 5 and the common difference is 3, what is the 4th term?

Back

The 4th term is 5 + (4 - 1) * 3 = 5 + 9 = 14.

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

How do you find the common difference in an arithmetic sequence?

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The common difference (d) can be found by subtracting any term from the subsequent term: d = a_(n+1) - a_n.

Front

What is the 6th number in the arithmetic sequence 13, 19, 25, ...?

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The 6th number is 43.

Front

What is the next number in the arithmetic sequence 13, 19, 25, ...?

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The next number is 31.

Front

If an arithmetic sequence has a first term of 10 and a common difference of 2, what is the 10th term?

Back

The 10th term is 10 + (10 - 1) * 2 = 10 + 18 = 28.

Front

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

Back

The sum (S_n) of the first n terms can be calculated using the formula: S_n = n/2 * (a_1 + a_n), where a_n is the nth term.

Front

If the first term of an arithmetic sequence is 4 and the common difference is -1, what is the 5th term?

Back

The 5th term is 4 + (5 - 1)(-1) = 4 - 4 = 0.