Math  /  Algebra

QuestionWrite the arithmetic sequence 17,13,9,5,-17,-13,-9,-5, \ldots in the standard form: an=a_{n}= \square

Studdy Solution

STEP 1

1. The sequence provided is an arithmetic sequence.
2. The standard form of an arithmetic sequence is given by an=a1+(n1)d a_n = a_1 + (n-1) \cdot d , where a1 a_1 is the first term and d d is the common difference.

STEP 2

1. Identify the first term and the common difference of the sequence.
2. Write the expression for the n n -th term using the standard form of an arithmetic sequence.

STEP 3

Identify the first term a1 a_1 of the sequence. The first term is the first number in the sequence:
a1=17 a_1 = -17

STEP 4

Determine the common difference d d of the sequence. The common difference is the difference between any two consecutive terms. Calculate it using the first two terms:
d=13(17)=13+17=4 d = -13 - (-17) = -13 + 17 = 4

STEP 5

Write the expression for the n n -th term using the standard form of an arithmetic sequence:
an=a1+(n1)d a_n = a_1 + (n-1) \cdot d
Substitute the values of a1 a_1 and d d :
an=17+(n1)4 a_n = -17 + (n-1) \cdot 4

STEP 6

Simplify the expression:
an=17+4n4 a_n = -17 + 4n - 4
Combine like terms:
an=4n21 a_n = 4n - 21
This is the standard form of the arithmetic sequence.

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