Question

Which sequence could be partially defined by the recursive formula f (n + 1) = f(n) + 2.5 for n ≥ 1?

2.5, 6.25, 15.625, 39.0625, …

2.5, 5, 10, 20

–10, –7.5, –5, –2.5, …

–10, –25, 62.5, 156.25

Answer 1

The sequence that could be partially defined by the given recursive formula is:

-10, -7.5 , -5 , -2.5 ,........

Explanation:

We are given a recursive formula as:

`f(n+1)=f(n)+2.5` for n≥1

Hence, from the given options we will check the difference of which sequence is: 2.5

A)

2.5, 6.25, 15.625, 39.0625, …

6.25-2.5=3.75

15.625-6.25=9.375

As we could see that the common difference is not 2.5

Hence, option: A is incorrect.

B)

2.5, 5, 10, 20

5-2.5=2.5

10-5=5

20-10=10

As the common difference is not 2.5.

Hence, option: B is incorrect.

C)

–10, –7.5, –5, –2.5, …

-7.5-(-10)=-7.5+10=2.5

-5-(-7.5)=5+7.5=2.5

and -2.5-(-5)=-2.5+5=2.5

As the common difference is 2.5.

Hence, option: C is correct.

D)

-10, -25 , 6.25 , 156.25

-25-(-10)=-25+10= -15

As the common difference is not 2.5

Hence, option: D is incorrect.

Answer 2

–10, –7.5, –5, –2.5, …

Is defined by the formula because the next term can be obtained by adding 2.5 to the current one.