Respuesta :
Answer:
[tex]a_n = 8n+8[/tex] represent the sequence 16,24,32,40...
Step-by-step explanation:
The sequence given is
16,24,32,40.
And the options given are
an=4n+1
an=8n+8
an=8n+16
We will check for all so as to find the correct expression.
In the given sequence the first term is 16,
i.e a1 = 16
1). We will check for an = 4n+1 whether the first term is 16 or not.
We will put the value of n as 1;
[tex]a_1= 4\times1+1= 4+1=5[/tex]
With this option we get the first term as 5 but in the given sequence first term is 16.
Hence this option is Incorrect.
2). We will check for an = 8n+8 whether the first term is 16 or not.
We will put the value of n as 1;
[tex]a_1= 8\times1+8= 8+8=16[/tex]
With this option we get the first term as 16 and in the given sequence also first term is 16.
Hence this option is correct.
3). We will check for an = 8n+16 whether the first term is 16 or not.
We will put the value of n as 1;
[tex]a_1= 8\times1+16= 8+16=24[/tex]
With this option we get the first term as 24 but in the given sequence first term is 16.
Hence this option is Incorrect.
Hence we can say that an = 8n+8 represent the sequence 16,24,32,40...
