Question

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

Answer 1

Answer: $\\\Rightarrow\ a_n=a_{n-1}-3$, where $a-1 = 7$

The next term is -8.

Step-by-step explanation:

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

Here, the first term is $a_1=7$

The second term is $a_2=4$

The difference =$a_2-a_1=4-7=-3$

Similarly,  $a_3-a_2=1-4=-3$

$a_4-a_3=-2-1=-3$ and so on.

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

$a_n=a_{n-1}+d$, where d is the common difference.

Since , d=-3

$\\\Rightarrow\ a_n=a_{n-1}-3$, where $a-1 = 7$

The next term of the sequence is $a_6=a_5-3=-5-3=-8$

Answer 2

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.