a sequence is defined recursively using the formula f(n + 1) = f(n) - 5. which sequence could be generated…

a sequence is defined recursively using the formula f(n + 1) = f(n) - 5. which sequence could be generated using this formula?\n1, -5, 25, -125, ...\n2, 10, 50, 250, ...\n3, -2, -7, -12, ...\n4, 9, 14, 19, ...

a sequence is defined recursively using the formula f(n + 1) = f(n) - 5. which sequence could be generated using this formula?\n1, -5, 25, -125, ...\n2, 10, 50, 250, ...\n3, -2, -7, -12, ...\n4, 9, 14, 19, ...

Answer

Explanation:

Step1: Analyze the formula

The formula $f(n + 1)=f(n)-5$ means each term is 5 less than the previous term.

Step2: Check each option

For option 1, $-5\div1=- 5$, it's a geometric - sequence, not correct. For option 2, $10\div2 = 5$, it's a geometric - sequence, not correct. For option 3, $-2-3=-5$, $-7-(-2)=-5$, $-12-(-7)=-5$, it satisfies the rule. For option 4, $9 - 4=5$, not $-5$, not correct.

Answer:

3, -2, -7, -12, ...