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.

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.