Arithmetic Sequences

This set of flashcards provides key definitions, formulas, and concepts related to arithmetic sequences.

What is an arithmetic sequence?

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

What do you use to find the order of a term whose value is x?

To find the order of the term whose value is x, we put Tn = x.

How do you find the first positive term in an arithmetic sequence?

To find the order of the first positive term in an arithmetic sequence, we set Tn > 0.

How do you find the first negative term in an arithmetic sequence?

To find the order of the first negative term in an arithmetic sequence, we set Tn < 0.

If three numbers in an arithmetic sequence are given, how should they be arranged to find their sum?

They should be arranged in the form (a - d, a, a + d).

What is the common difference in the arithmetic sequence (5, 9, 13, 17)?

The common difference is 4.

What is the common difference in the arithmetic sequence (-17, -15, -13, -11)?

The common difference is 2.

How do you determine if a sequence defined as (Tn) = (3n - 2) is arithmetic?

If (Tn+1) - (Tn) results in a constant, then the sequence is arithmetic.

In the sequence (95, 92, 89, …), what is the value of T6?

T6 is 80.

Is there a term in the arithmetic sequence (-42, -39, -36, …, 21) whose value is -11?

No, there is no term whose value is -11.

What is the relationship between T2 and T4 for the sequence defined in EX(6)?

T2 + T4 = 2T3.

In the arithmetic sequence where T2 = 576 and T+7 = 405, what can you infer?

You can set up equations to find the values of a and d to determine the arithmetic sequence.

What is the formula to find the nth term in an arithmetic sequence?

The nth term is given by Tn = a + (n - 1)d.

How can you find the last term in a given arithmetic sequence?

You sum the first term and the product of the common difference and the total number of terms.