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 (d) is the fixed amount added to each term to get the next term in the sequence.

Front

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

Back

The nth term (a_n) 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 26th term in the arithmetic sequence: -15, -35, -55, -75, ...

Back

a_26 = -15 + (26-1)(-20) = -515.

Front

Find the 22nd term of the sequence: 5, 8, 11, ...

Back

a_22 = 5 + (22-1)(3) = 68.

Front

Find the 26th term in the arithmetic sequence: 20, 26, 32, 38, ...

Back

a_26 = 20 + (26-1)(6) = 170.

Front

What is the formula to find the common difference?

Back

The common difference can be found using: d = a_n - a_(n-1), where a_n is the nth term and a_(n-1) is the previous term.

Front

Find the common difference in the sequence: 29, 21, 13, 5, ...

Back

d = 21 - 29 = -8.

Front

Is the sequence 21, 13, 5, -3, ... arithmetic?

Back

YES, the common difference is -8.

Front

What is the first term of an arithmetic sequence?

Back

The first term (a_1) is the initial term of the sequence from which all other terms are derived.