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In an arithmetic sequence, a14=-75 and a26=-123 Which recursive formula defines the sequence?
A. an=an-1-4;a1=-23
B. an=an-1-4;a1=-19
C. an=-4an-1-19;a1=-23
D. an=-4an-1-19;a1=-19

Respuesta :

SociometricStar

Answer:

[tex]a_n=a_{n-1}-4,a_1=-23[/tex]

A is the correct option.

Step-by-step explanation:

We have been given that [tex]a_{14}=-75,a_{26}=-123[/tex]

The general term of an arithmetic sequence is given by

[tex]a_n=a+(n-1)d[/tex]

Now, for 14th term,

[tex]a_{14}=a+(14-1)d\\a+13d=-75.....(1)[/tex]

Similarly, for 26th term

[tex]a_{26}=a+(26-1)d\\a+25d=-123.....(1)[/tex]

Subtract equation 1 and 2

[tex]-12d=48\\d=-4[/tex]

From equation 1

[tex]a-52=-75\\a=-23[/tex]

Hence, the first term is [tex]a_1=-23[/tex]

Now, since the common difference d is -4.

Hence, the recursive formula is

[tex]a_n=a_{n-1}-4,a_1=-23[/tex]

abidemiokin

The recursive formula that defines the sequence is an=an-1-4 with  the first term as -23

Sequence and series

Sequences are values arranged in a pattern. The nth term of an arithmetic sequence is expressed as:

Tn = a + (n - 1) d

If in an arithmetic sequence, a14=-75 and a26=-123, then:

a + 13d = -75
a + 25d = -123

Subtract the equations

13d - 25d = -75 + 123
-12d = 48
d = -4

Determine the first term

a + 13d = -75
a + 13(-4) = -75
a - 52 = -75
a = -23

Since the common difference is -4, the recursive formula is expressed as:

an=an-1 + d
an = an-1 - 4; a1 = -23

Hence the recursive formula that defines the sequence is an=an-1-4 with  the first term as -23

Learn more on sequence here: https://brainly.com/question/6561461

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