Question

The first four terms of a sequence are shown below: 7, 4, 1, -2 Which of the following functions best defines this sequence? A.f(1) = 7, f(n + 1) = f(n) + 3; for n ≥ 1 B.f(1) = 7, f(n + 1) = f(n) - 3; for n ≥ 1 C.  f(1) = 7, f(n + 1) = f(n) - 4; for n ≥ 1 D.f(1) = 7, f(n + 1) = f(n) + 4; for n ≥ 1

Answer 1

answer is B.f(1) = 7, f(n + 1) = f(n) - 3; for n ≥ 1

f(1) = 7
f(2) = 7 -3 = 4
f(3) = 4 -3 = 1
f(4) = 1 -3 = -2

Answer 2

Option (B) is correct.

The sequence that best defines the function is f(1) = 7, f(n + 1) = f(n) - 3; for n ≥ 1

Explanation:

Given sequence 7 ,4, 1,-2

We have to choose a function from given options that best defines this sequence.

Let f(n) denotes the value at nth position,

Like f(1) = 7 , so here, n= 1.

Since next term is 4 = f(2)

4 can be written as 7 - 3 = f(1) -3

Next term is 1 = f(3)

1 can be written as 4-1 = f(2) - 3

Next term is -2 = f(4)

-2 can be written as 1-3 = f(3) - 3

Thus, following the sequence and writing in general form for n

f(n+1) = f (n) -3 , n ≥ 1

Thus, option (B) is correct.

The sequence that best defines the function is f(1) = 7, f(n + 1) = f(n) - 3; for n ≥ 1