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Write a recursive formula for the sequence 7, 4, 1, –2, –5, .... Then find the next term. (1 point) an = an–1 – 3, where a1 = –8; 7 an = an–1 – 3, where a1 = 7; –8 an = an–1 + 3, where a1 = –3; 22 an = an–1 + 3, where a1 = 7; –8

Respuesta :

Edufirst
4 = 7 - 3

1 = 4 - 3

-2 = 1 - 3

-5 = -2 - 3

=> An = A (n-1) - 3, where A1 = 7

The next term is A6 = A5 - 3 = - 5 - 3 = - 8

So the answer is the fourth option.
JeanaShupp

Answer: [tex]\\\Rightarrow\ a_n=a_{n-1}-3[/tex], where [tex]a-1 = 7[/tex]

The next term is -8.

Step-by-step explanation:

The given sequence is 7, 4, 1, –2, –5, ................

Here, the first term is [tex]a_1=7[/tex]

The second term is [tex]a_2=4[/tex]

The difference =[tex]a_2-a_1=4-7=-3[/tex]

Similarly,  [tex]a_3-a_2=1-4=-3[/tex]

[tex]a_4-a_3=-2-1=-3[/tex] and so on.

Therefore, the recursive formula for the above sequence will be given by :-

[tex]a_n=a_{n-1}+d[/tex], where d is the common difference.

Since , d=-3

[tex]\\\Rightarrow\ a_n=a_{n-1}-3[/tex], where [tex]a-1 = 7[/tex]

The next term of the sequence is [tex]a_6=a_5-3=-5-3=-8[/tex]

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